Asymmetric dark matter
in braneworld cosmology
Abstract
We investigate the effect of a braneworld expansion era on the relic density of asymmetric dark matter. We find that the enhanced expansion rate in the early universe predicted by the Randall-Sundrum II (RSII) model leads to earlier particle freeze-out and an enhanced relic density. This effect has been observed previously by Okada and Seto (2004) for symmetric dark matter models and here we extend their results to the case of asymmetric dark matter. We also discuss the enhanced asymmetric annihilation rate in the braneworld scenario and its implications for indirect detection experiments.
James Cook University,
1 James Cook Dr.
QLD, 4811, Australia
\emailAddMichael.M
\emailAddIan.W
1 Introduction
Despite the overwhelming astrophysical and cosmological evidence for the existence of Dark Matter (DM) [1], very little is known about its particle nature. Many particle candidates have been proposed which are capable of explaining the observational data yet none have been conclusively verified. The data favour cold (non-relativistic) DM for which the most popular theoretical candidates are WIMPs (Weakly Interacting Massive Particles) with mass GeV. Supersymmetric extensions of the Standard Model (SM) in which -parity is conserved provide a viable DM candidate, the neutralino, which is the lightest supersymmetric particle formed from higgsinos and weak gauginos and is stable against decay into SM particles.
A popular framework for the origin of dark matter is provided by the thermal relic scenario; at early times, when the temperature of the universe is high, frequent interactions keep the dark matter (anti) particles, , in equilibrium with the background cosmic bath. As the universe expands and cools the dark matter interaction rate drops below the expansion rate and the particles fall out of equilibrium. Eventually both creation and annihilation processes cease, and the number density redshifts with the expansion. This is known as particle freeze-out, and the remaining ’relic’ particles constitute the dark matter density we observe today.
A combined analysis of the Planck satellite + WP + highL + BAO measurements gives the present dark matter density as ( C.L.) [2]
(1) |
where and is defined by the value of the Hubble constant, km/s/Mpc.
Due to the Boltzmann suppression factor in the equilibrium number density, the longer the DM (anti) particles remain in equilibrium the lower their number densities are at freeze-out. Thus species with larger interaction cross sections which maintain thermal contact longer, freeze out with diminished abundances. Thermal relic WIMPS are excellent DM candidates as their weak scale cross section gives the correct order of magnitude for for a standard radiation-dominated early universe. However, if the universe experiences a non-standard expansion law during the epoch of dark matter decoupling, freeze-out may be accelerated and the relic abundance enhanced [3, 31].
The physics of the early universe, prior to the era of Big Bang Nucleosynthesis (BBN), is relatively unconstrained by current observational datasets. Dark matter particles, which decouple from the background thermal bath at early times, carry the signature of these earliest moments and therefore provide an excellent observational probe. If the properties of the dark matter particles are ever discovered, either through direct/indirect detection experiments or via particle creation in particle accelerators [4], then relic abundance calculations could provide a valuable insight into the conditions of the universe prior to BBN.
The majority of dark matter models assume symmetric dark matter for which the particles are Majorana fermions with , i.e. they are self-conjugate. Given that most known particles are not Majorana, it is natural to consider asymmetric dark matter models in which the particle and antiparticle are distinct, i.e. , and to assume an asymmetry between the number densities of the DM particles and antiparticles. Indeed, a similar asymmetry exists in the baryonic matter sector between the number of observed baryons and antibaryons . This baryonic asymmetry is
(2) |
where is the number density of photons. Several models have been proposed [5] that relate the asymmetries in the baryonic and dark sectors. These models typically assume [6] either a primordial asymmetry in one sector which is transferred to the other sector, or that both asymmetries are generated by the same physical process such as the decay of a heavy particle. Kaplan et al. [7] consider a baryonic asymmetry generated by baryogenesis at high temperatures that is transferred to the DM sector by interactions arising from higher dimension operators which then decouple at a temperature above the DM mass and freeze in the asymmetry. If the asymmetries in the dark and baryonic matter sectors share a common origin then their number densities will be related , as will their densities [7]. This could explain the approximate equality of the observed dark and baryonic abundances () and suggests a WIMP mass in the range GeV. Interestingly, this mass range is favored by a number of observational datasets [9, 10, 8] providing further motivation for asymmetric DM.
Cosmological, astrophysical and collider constraints on light thermal DM (1 MeV - 10 GeV) have been examined by [11] for both symmetric and asymmetric models of DM and [12] have considered flavour constraints on, and collider signatures of, asymmetric DM produced by decays of supersymmetric particles in the minimal supersymmetric Standard Model.
The relic abundance of asymmetric DM has been studied [15, 13, 14] in the standard cosmological scenario and for the non-standard quintessence scenario in which a non-interacting scalar field is present in its kination phase. Gelmini et al. [15] also considered a simple scalar-tensor cosmology parameterized as a multiplicatively modified Hubble expansion. The enhanced expansion rate predicted by each non-standard scenario led to earlier particle freeze-out and an enhanced relic abundance. As a result, the asymmetry between the particles and antiparticles was essentially ’washed out’.
In this study we consider the effect of an early time braneworld expansion era on the present density of asymmetric dark matter. Braneworld models are toy models arising from string theory where additional spacetime dimensions are incorporated in an attempt to unify the fundamental forces of nature. In the braneworld scenario, our universe is modeled as a dimensional surface (the brane) embedded in a higher dimensional spacetime known as the bulk. The standard model particles are confined to the surface of the brane whilst gravity resides in the higher dimensional bulk. This offers an explanation for the apparent weakness of gravity with respect to the other fundamental forces [16].
The effect of a braneworld expansion era on the relic abundance of symmetric DM has been studied by [17, 18, 19, 20, 21]. They found that the modified expansion rate in braneworld models led to earlier particle freeze-out and an enhanced relic abundance (provided the five-dimensional Planck mass is low enough), similar features to those of the quintessence and scalar-tensor scenarios. We report here an extension of these studies to the case of asymmetric DM.
In the next section we introduce the Randall-Sundrum type II braneworld model and its relevant parameters. Then in section 3 we present the Boltzmann equations which describe the time evolution of the asymmetric DM number densities and give both numerical and analytical solutions for the braneworld case. We constrain the possible parameter combinations using the observed DM density (1) in section 4 before discussing the asymmetric DM annihilation rate and prospects for indirect detection of asymmetric DM in sections 5 and 6 respectively. Finally we summarize our findings in section 7.
2 Braneworld model
In this work we focus on the Randall-Sundrum II (RSII) model [22] in which our universe is realized on a -Minkowski brane with positive tension, located at the ultraviolet boundary of the five dimensional anti-de Sitter bulk with cosmological constant . The expansion rate in this model is given by the modified Friedmann equation,
(3) |
where is the brane tension, the four-dimensional cosmological constant has been fine-tuned to zero and is the five dimensional Planck mass which we will treat as a free parameter. The four dimensional Planck mass GeV is related to Newton’s constant by . We have omitted the so-called ’dark radiation’ term (where is the cosmic scale factor) because of the severe constraints on extra light degrees of freedom at the time of Big Bang Nucleosynthesis [23].
A novel feature of (3) is the presence of the term quadratic in . At high energies () this term dominates the expansion and . Comparing this to the standard scenario where we see that the early time expansion rate is enhanced in the RSII braneworld model. As the energy density drops () the quadratic term becomes negligible and the standard expansion law is recovered.
Since the early universe is radiation dominated, the energy density is , where counts the number of relativistic degrees of freedom at temperature ^{1}^{1}1Since the number of relativistic degrees of freedom only differs from the number of entropic degrees of freedom when the temperature crosses a mass threshold, we take throughout., and we can rewrite the modified Friedmann equation as
(4) |
where is the expansion rate for the standard General Relativity scenario, and
(5) |
The parameter denotes the transition point from the brane expansion era to the standard expansion era. We note that smaller values of give a larger and a greater departure from the standard expansion history.
To preserve the successful predictions of Big Bang Nucleosynthesis we must ensure that the standard expansion rate is restored before MeV. This translates to a transition point of where is the DM mass in units of 100 GeV. In terms of the parameter we require GeV ^{2}^{2}2More stringent constraints have been placed on from sub-millimeter measurements of the gravitational force and the requirement of a vanishing cosmological constant, however these constraints are sensitive to the presence of a bulk scalar field [24] and will not be considered here..
In order to modify the canonical relic abundance result the DM particles must freeze-out before the standard expansion rate is restored. The standard freeze-out point depends only logarithmically on the DM mass [25] whereas, from (5), the transition point, , is proportional to the DM mass. The braneworld effects will therefore be more exaggerated for larger masses. Conversely, if the DM mass is small, a larger transition point is required to modify the relic abundance.
3 Asymmetric dark matter
3.1 Relic density
The relic density of asymmetric DM is obtained by solving the relevant Boltzmann equations for the particle and antiparticle . Assuming that the only annihilation processes are those of pairs into Standard Model particles, that is there is no self-annihilation involving or pairs, the time evolution of the number densities are given by the coupled system of Boltzmann equations
(6) | ||||
(7) |
where is the expansion rate of the universe, is the thermally averaged annihilation cross section multiplied by the relative velocity of the annihilating pair (loosely termed the "annihilation cross section") and are the equilibrium number densities of the particle and antiparticle components. Assuming the DM particles are non-relativistic at decoupling, the equilibrium densities are
(8) | ||||
(9) |
where is the number of internal degrees of freedom of and we have used the fact that, in equilibrium, the chemical potentials and satisfy .
The thermally averaged annihilation cross section is generally parameterized as
(10) |
where the constant term, , corresponds to -wave scattering and the temperature dependent term, , to -wave scattering. Throughout this work we assume that annihilations are dominated by wave processes and set .
It is convenient to rewrite the Boltzmann equations in terms of the dimensionless variables and , where is the entropy density. The system (7) tranforms to
(11) |
where the coefficient is defined as
(12) |
and is a temperature dependent variable related to the change in the number of degrees of freedom
(13) |
Assuming that the entropy density is conserved (i.e. const.) the variable may be interpreted as the comoving number density of the particle (antiparticle) component^{3}^{3}3Many authors neglect the temperature evolution of and set . However, as pointed out by [26], the temperature dependence of these terms may have an appreciable effect on the final relic density. For braneworld models in particular, annihilations can persist for an extended period after particle freeze-out before the number density reaches its asymptotic value [17]. During this time the value of may vary by up to an order of magnitude and the resulting relic density can be out by a factor of 2 if the full temperature dependence of this term is not maintained. In what follows we only fix the number of relativistic degrees of freedom (and in turn set ) in order to derive analytic solutions to the Boltzmann equations. However, in our numerical analysis, the full temperature dependence is maintained..
Since we have assumed that only interactions of the type (where denotes a standard model particle) can change the particle number, we can write
(14) |
where is a strictly positive constant which defines the asymmetry between the particles and antiparticles . We have assumed that is the majority component and the minority component. Here, we are not particularly interested in the mechanism which generates the asymmetry, only that the asymmetry has been created well before particle freeze-out^{4}^{4}4If the asymmetry in the dark sector is linked to the baryonic asymmetry as discussed in the introduction, we would expect that . Using the present entropy density [27] gives an estimate for the dark sector asymmetry, ..
The Boltzmann equations (11) can then be written
(15) |
where
(16) |
The present day DM density is determined by solving the system (15) in the limit with the total density being the sum of the and densities
(17) |
where . Note that setting only establishes an equality between the particle and antiparticle number densities, i.e. . The particles and anti-particles are still distinct and they must be counted separately. For this reason the annihilation cross section needed to produce the observed DM abundance in asymmetric models with is typically twice that of the symmetric case.
Using (14), we also see that the introduction of an asymmetry places a lower bound on the relic density with . This is a characteristic feature of asymmetric models in which the relic abundance is typically fixed by the asymmetry, , as opposed to the symmetric case where the annihilation cross section, , determines the final density.
In the coming sections we will see that, if DM particle freeze-out occurs during a braneworld expansion era, not only is the relic density enhanced with respect to the canonical result, but that the asymmetric DM behaves very much like symmetric DM in that the relic density is determined by the annihilation cross section and is independent of the asymmetry.
3.2 Density evolution
The evolution of the comoving number density in the braneworld scenario is determined from the system of Boltzmann equations (15) with the expansion rate in the factor obtained from the modified Freidmann equation (3). Numerical solution of the equations was performed for an asymmetry and a WIMP with mass GeV, and annihilation cross section cms. The results are shown in Figure 1. We have considered the two cases; GeV and GeV (recall that smaller values of represent a greater departure from the standard expansion history). The density evolution in the standard scenario is also shown for reference.
Initially both the and components are in equilibrium and track their equilibrium number densities . As the universe expands, the interaction rate drops below the expansion rate and the (anti)particles depart from equilibrium. The freeze-out point is in the standard scenario. From Figure 1 we see that the modified expansion rate in the braneworld cosmology leads to earlier particle freeze-out ( for GeV and for GeV). There is also an enhanced relic density. A comparison of the left and right panels shows the effects are amplified for smaller values of with the relic density being boosted by a factor of and for GeV and GeV respectively.
With the enhanced relic density, the asymmetry between the particles and antiparticles is essentially ’washed’ out by the braneworld expansion era. Again this effect is most noticeable for smaller values of as can be seen in the right panel of Figure 1 where the number densities of the and components coincide.
An interesting feature of Figure 1 is the evolution of the comoving number densities in the braneworld cosmology after particle freeze-out. The densities of the majority and minority components continue to decay even after decoupling and do not reach their asymptotic values until well after freeze-out. This behavior is characteristic of the RSII braneworld model where the asymptotic density is not reached until the standard expansion rate is restored [17], which for GeV and GeV occurs at and respectively^{5}^{5}5For the interval the comoving density in the braneworld cosmology behaves approximately as [17].. This highlights the importance of maintaining the temperature dependence of in the numerical calculation.
3.3 Analytical solution
Although the Boltzmann equations (15) can not be solved exactly using analytical methods, we can find approximate solutions in limiting cases. For example, once the DM species has decoupled from the background thermal bath, the comoving number density due to the exponential decay of the equilibrium density (see Fig. 1). Hence the creation term proportional to in (15) can be neglected for (where and are the freeze-out points of the particle and antiparticle components respectively) and the reduced expressions can be integrated directly to yield [13]
(18) | ||||
(19) |
where
(20) |
The subscript in is used to indicate that (20) is the asymptotic solution for a symmetric DM species ^{6}^{6}6The Boltzmann equation for a symmetric DM species, , is given by,
The density of the and components depends sensitively on the ratio . For large values of this ratio the contribution from the minority component () is exponentially suppressed and the density of the majority component approaches the asymmetry, . When this ratio is small, the asymmetry drops out of the expressions (18) and (19) and each component behaves like symmetric dark matter, . This second case is illustrated in the right panel of Figure 1 where the braneworld expansion rate has boosted the value of such that the and densities are indistinguishable. The important quantity is the ratio , so that even for large asymmetries the asymmetric DM can appear symmetric if the magnitude of is large enough.
Substituting (18) and (19) into (17) we obtain an approximate expression for the relic density ,
(21) |
which in the two limiting cases discussed above becomes,
(22) |
So far in this subsection we have not made any reference to the specific form of the integrand in (20). This means that the arguments which have been developed can be applied to any cosmological scenario in which the relic density obeys (15). Indeed these effects have already been demonstrated for the quintessence [15, 14] and scalar-tensor [15] scenarios. Both of these models predict an enhanced expansion rate at the epoch of dark matter decoupling which was found to ’wash out’ the asymmetry between the particles and antiparticles.
Focusing on the RSII braneworld cosmology, the integral (20) has been computed in [17] for the expansion rate (3) and in the limit becomes^{7}^{7}7To evaluate the integral (20) the number of relativistic degrees of freedom has been fixed, i.e. const. We find that the most appropriate value of in the analytic expressions (23) and (24) is given by and respectively, where is the transition temperature and is the freeze-out temperature.
(23) |
This expression is only valid if particle freeze-out occurs during the braneworld era . Thus, for smaller mass particles (which freeze out at lower temperatures), a later transition point (smaller ), is required for this approximation to hold. If DM decoupling occurs after the transition point, when the RSII expansion rate has reduced to the standard one, the canonical result is recovered,
(24) |
where is the freeze-out point in the standard scenario. Inserting (23) into (18) and (19) we see that, if either the annihilation cross section or the value of is large, we expect the component to be exponentially suppressed, provided that , and the density of the majority component to be fixed by the asymmetry, . If and are small, such that (and ), then the dark matter particles behave like symmetric dark matter and the relic density, using (22), is given by,
(25) |
Comparing the relic density in the braneworld case with the standard cosmology result, we see that the abundance is boosted by a factor of [17],
(26) |
Therefore larger values of the transition point will result in greater enhancements of the DM relic abundance as we expected. To compensate, the annihilation cross section will have to be increased in order to provide the observed relic abundance (1).
4 Relic density constraints
The magnitude of the five dimensional Planck mass, , and the asymmetry, , can be constrained by the observed DM relic density (1). In Figure 2 we plot the contours in the plane which give the correct relic abundance for varying . The red and green curves correspond to GeV and GeV respectively and the blue curve gives the standard cosmology result. We have considered both GeV (solid) and GeV (dashed).
Two distinct regions are apparent. In the first, the curves are vertical and the relic abundance is independent of the asymmetry. In this region the ratio is small and the and components behave like symmetric DM where the density is determined by the annihilation cross section, see (22), (23) and(24). As the asymmetry increases so does the magnitude of the ratio and the contours transition into a region which is strongly asymmetric, i.e. the relic density is now fixed by the asymmetry and is independent of the annihilation cross section. In this regime the density of the minority component is exponentially suppressed and the DM abundance is given by . For the observed density (1) this occurs at ^{8}^{8}8There is also an intermediate region where the abundance depends on both the asymmetry and the annihilation cross section. Here the minority component freezes out shortly after the majority component and their final densities are comparable. For a discussion on each regime and their relation to the freeze-out of the and components see [15]..
Each of the iso-abundance contours is accurately described by the relation,
(27) |
where ^{9}^{9}9Again, this will be true of any cosmology in which the symmetric solution .. The appropriate form of (27) depends on whether we are in the region or , in which case we would use the approximate formulas (23) or (24) respectively. In the first case, freeze-out occurs prior to the transition point and the annihilation cross section is shifted to larger values as the magnitude of decreases (or as increases). The shift is more pronounced for the GeV case since these particles freeze-out earlier compared to the GeV particles (see the discussion in section 2).
Using the observed relic density (1) we can also determine the required annihilation cross section as a function of the five dimensional Planck mass . These results are shown in Figure 3 for different values of the asymmetry . The left panel corresponds to a WIMP with mass GeV and the right panel to GeV. In each plot we see that the required annihilation cross section is increased by up to several orders of magnitude compared to the standard result (see the blue curves in Figure 2).
From the earlier discussion (see section 2) we recall that the annihilation cross section is only enhanced if freeze-out occurs during a braneworld type expansion era, i.e. for . In the standard cosmology freeze-out occurs at approximately so we require . Using the definition of , (5), this corresponds to GeV and GeV for GeV and GeV respectively. In this region the curves approximately obey
(28) |
For larger values of (smaller ) the standard expansion law is recovered prior to DM decoupling and the curves saturate to the standard result.
5 Annihilation rate for asymmetric DM
The modified expansion rate in the braneworld scenario requires an enhanced annihilation cross section in order to provide the observed DM density. In this section we discuss the impact this result has on the annihilation rate of asymmetric DM, . We find that although the density of the minority component is exponentially suppressed in asymmetric DM models, the increased annihilation cross section may compensate for this and produce an amplified detection signal. This effect has been pointed out by [15] for the kination and scalar-tensor scenarios and is in contrast to the usual expectation that the asymmetric signal is reduced with respect to the symmetric one.
To compare the expected detection signals in the two cases we first write the annihilation rate of symmetric dark matter in the standard scenario [15],
(29) |
where is the self annihilation cross section of the self-conjugate particles in the standard cosmological scenario, is the DM energy density, (where is the critical density), and the factor of is necessary since the annihilating particles are identical. The required annihilation cross section in the standard scenario is found numerically to be cms for GeV and cms for GeV.
The annihilation rate for asymmetric dark matter in the braneworld scenario can be written, using (14) and (17), as
(30) |
and the ratio of the two annihilation rates is then
(31) |
Once the relic density has been specified, the damping factor can be expressed explicitly in terms of the asymmetry ;
(32) |
where . The magnitude of this factor varies from for small to at . This relationship has been plotted in Figure 4 for the observed DM density (1) where we see that, for , the damping factor and then rapidly drops to zero thereafter.
Given that the required annihilation cross section can be several orders of magnitude larger in the braneworld scenario compared to the symmetric one in the standard cosmology (see Figure 3), the ratio of the annihilation cross sections in (31) can easily compensate for the asymmetric damping factor for a large range of asymmetries, .
The ratio , given by (31), can be evaluated using the cross sections calculated in the previous section. This ratio is shown in Figure 5 as a function of for different values of the asymmetry . As predicted, the asymmetric annihilation rate in the braneworld scenario can exceed the symmetric one in the standard scenario for a significant region of the parameter space. In particular we find that, for and GeV, the asymmetric signal is times larger than the symmetric signal in the standard cosmology for GeV. Even larger asymmetries such as can produce a signal enhanced by a factor of for GeV.
Although enhanced signals for asymmetric DM are possible in the braneworld scenario for certain parameter combinations, it is important to check that such combinations satisfy the observational constraints on the DM annihilation cross section. In the next section we review our results in light of the gamma ray data from the Fermi space telescope.
6 Fermi-LAT constraints
In addition to the relic density observation, data is available from the Fermi Large Area Telescope (Fermi-LAT) which searches for gamma rays from satellite galaxies of the Milky Way, such as those originating from DM annihilations [28]. Depending on the annihilation channel, the gamma ray data can be used to place upper bounds on the DM annihilation cross section assuming the DM species constitutes all of the DM density. Therefore, the predicted asymmetric detection signal will satisfy the Fermi bound if,
(33) |
where is the inferred cross section bound from the Fermi gamma ray data. In terms of the asymmetric annihilation cross section, , and asymmetry, , this condition can be expressed as (using (31)),
(34) |
In Figure 6 we superimpose these constraints on the iso-abundance contours of Figure 2 (the constraints are shown as the pink dashed curves with the area beneath the curves excluded for that particular annihilation channel). For illustration we have only displayed the bounds for the and channels which, for a WIMP with mass GeV, are cms and cms respectively. For the GeV case the bounds are more stringent with cms and cms for the respective channels.
The results in Figure 5 should be compared with the constraints displayed in Figure 6 in order to determine which combinations of and simultaneously satisfy the Fermi bounds whilst predicting an enhanced detection signal, . For example, for the combination GeV and GeV, we see from the right panel of Figure 6 that all values of the asymmetry are permitted by the Fermi-LAT data. Then, from the right panel of Figure 5 we can see that for this value of , the asymmetric annihilation rate is amplified, , for asymmetries up to . In general, it is possible to have an enhanced annihilation rate which is consistent with the Fermi-LAT data, if the asymmetric annihilation cross section, , and asymmetry , satisfy
(35) |
where is the damping factor defined in (32). This region is plotted in Fig. 7 and depends upon the appropriate annihilation channel.
7 Conclusions
In this article we have investigated the relic density and observational signatures of asymmetric dark matter models in the braneworld cosmology. We have found that the decoupling of asymmetric dark matter and the evolution of the particle/antiparticle number densities is modified in the RSII braneworld scenario. In particular, the enhanced braneworld expansion rate leads to earlier particle freeze-out and an enhanced relic density. Additionally, the asymmetry between the DM particles and antiparticles is ’washed’ out by the modified expansion rate and the relic abundance is determined by the annihilation cross section . In this respect the nominally asymmetric model behaves like symmetric dark matter. This effect was demonstrated analytically in section 3.3 where we derived approximate expressions for the densities of the majority and minority DM components in the braneworld scenario and is consistent with other investigations of asymmetric dark matter in non-standard cosmologies which predict an enhanced expansion rate during the epoch of dark matter decoupling [15, 14].
Importantly, we have also accounted for the variation in the number of relativistic degrees of freedom as a function of temperature, , in our numerical solution of the Boltzmann equation. This variation is particularly pertinent for the RSII braneworld model in which asymptotic behaviour of the number densities is not achieved until well after decoupling. Fixing const. in the numerical integration can result in relic density predictions which are out by a factor of depending on the magnitude of .
Finally, in order to provide the observed relic density (1) the annihilation cross section must be boosted to compensate for the enhanced expansion rate. In this instance we find that the annihilation rate, , of asymmetric DM in the braneworld cosmology is larger than the symmetric signal in the standard scenario despite the suppressed abundance of the minority DM component. This effect is contrary to the usual expectation which presumes a weaker asymmetric detection signal. We have also shown that it is possible to produce an amplified asymmetric detection signal which satisfies the observational constraints from Fermi-LAT [28].
Additional data from Fermi-LAT and other indirect detection probes [29, 30] may further constrain the dark matter particle properties and in the process shed light on the cosmological conditions prior to BBN.
Very recently new information about the very early universe has been provided by the BICEP2 experiment [32] which detected -mode polarization of the CMB, indicating a large tensor-to-scalar ratio . These primordial tensor perturbations are strong evidence of gravitational waves and are a generic prediction of inflationary cosmological models with large energy density [33, 34]. Whereas the BICEP2 result of for the infrared tilt of the scalar perturbations is in agreement with Planck [46] and WMAP and supports slow roll models of inflation, the BICEP2 result for is in some tension with the Planck observations [35] that give and which favour Starobinsky inflation [36, 37] that predicts . The BICEP2 value for is consistent with simple single scalar field models of chaotic inflation with a quadratic self-interaction [38] that predict . Although aspects of the BICEP2 analysis require further investigation, if the BICEP2 result for is confirmed then it is of interest to note that such a value follows naturally from RSII braneworld cosmology. Slow roll chaotic inflation in RSII braneworld cosmologies for a single field with a monomial potential has been the subject of several investigations. Although early studies [39, 40] found that the ratio of tensor-to-scalar modes was suppressed for inflation at high energy scales , subsequent investigations [41, 42, 43, 44, 45] found instead an enhancement. Specifically, the spectral index, , and tensor-to-scalar ratio, , in the RSII braneworld scenario are given respectively by
where is the number of -folds^{10}^{10}10Slightly different forms of the denominator in the expression for are given in the literature. For example, [41] give whereas [44, 45] give .. For a quadratic potential and , the values of and agree closely with the BICEP2 result.
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