Exotic Recombination

Nuclear Physics B (Proc. Suppl.) 194 (2009) 57–62 www.elsevier.com/locate/npbps

Exotic Recombination Silvia Gallia a

Physics Department, Universita’ di Roma “La Sapienza”, Ple Aldo Moro 2, 00185, Rome, Italy Laboratoire Astroparticule et Cosmologie (APC), Universite’ Paris Diderot - 75205 PARIS cedex 13. I review few examples of the numerous physical processes that might change the standard model of recombination. The high precision of current and future CMB data may allow the detection of these processes, that leave recognizable imprints on the angular power spectra. I review some of the results obtained in constraining i) a variation of the gravitational constant G ii) the presence of extra-sources of energetic photons in the primeval plasma and iii) annihilation of dark matter particles.

1. Introduction The recent measurements of the Cosmic Microwave Background (CMB) flux provided by the five year Wilkinson Microwave Anisotropy Probe (WMAP) mission (see [1,2] and the ACBAR collaboration (see [3]) have confirmed several aspects of the cosmological standard model and improved the constraints on several key parameters. These spectacular results, apart from the experimental improvements, have been possible due to the high precision of the CMB theoretical predictions that have now reached an accuracy close to 0.1% over a wide range of scales. A key ingredient in the CMB precision cosmology is the accurate computation of the recombination process. Since the seminal papers by Peebles and Z’eldovich (see [4,5]) detailing the recombination process, further refinements to the standard scheme were developed [6] allowing predictions at the accuracy level found in data from the WMAP satellite and predicted for the Planck satellite [7–9]. While the attained accuracy on the recombination process is impressive, it should be noticed that these computations rely on the assumption of standard physics. Non-standard mechanisms could produce extra sources of radiation or determine a variation of fundamental constants, therefore yielding a modification of the recombination process. With the WMAP results and the future Planck data, it therefore becomes conceivable that deviations from standard recombination 0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.07.083

may be detected. Here I want to focus on few examples of the extremely vast possible non-standard scenarios that might affect the physics of recombination, showing how much current and future CMB data can constrain these models. Most of the work presented here is taken from [10], [11] and [12]. I refer the reader to those papers for more details. 2. Varying constants The hyphotesis that fundamental constants of physics could vary in space and time was probably first proposed by Dirac [13]. Since then, many authors have explored this possibility (see [14] for a complete review), improving the accuracy on the value of these constants. Many different methods have been used to test the constancy of these quantities at different scales and epochs. Nevertheless, it is still difficult to determine some of them with very high precision. In particular, the gravitational constant G remains one of the most elusive constants in physics. The past two decades did not succeed in substantially improving our knowledge of its value from the precision of 0.05% reached in 1942 (see [15]). To the contrary, the variation between different measurements forced the CODATA committee1 , which determines the internationally accepted standard values, to increase the uncertainty from 0.013% for the value quoted in 1987 to the one order 1 See

http://www.codata.org/

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of magnitude larger uncertainty of 0.15% for the 1998 ”official” value ([16]). Measurements of the Cosmic Microwave Background temperature and polarization anisotropy have been suggested as a possible tool for determining the value of the gravitational constant G (see [17]). In [10] we have constrained the value of G using WMAP05 and ACBAR data and simulated data for the PLANCK satellite and for a hypotetical cosmic variance limited experiment. We have first determined the constraints on a constant value of G using current CMB data. We have parameterized the deviations from the conventional value of the gravitational constant G0 by introducing a dimensionless parameter λG such that G = G0 λ2G following [17]. We have then allowed λG to vary in a modified version of the CAMB code ([19]) in the publicly available Markov Chain Monte Carlo package cosmomc ([20]). Results for different sets of data are shown in table 1.

in time of G. Many theories, such as scalar-tensor models of gravity (see for example [21]), provide precise predictions for the evolution of G with time and space. Nevertheless, we have chosen to follow a phenomenological approach, supposing a simple linear evolution of the G constant with the scale factor a: G = G0 + G0 (λ2G − 1)(1 − a)

(1)

where G0 is the value measured nowadays. Constraints on λG appear to be more stringent in this model than the ones obtained in the case of a constant G, λG = 1.01 ± 0.1 at 68% c.l.. This is due to the fact that a variation in G leads to a time-variation of the gravitational potential, therefore producing a very strong integrated Sachs-Wolfe effect on the spectra. As this kind of signal is at odds with current CMB data, the constraints on this model turn out to be stronger.

3. Extra-photons during recombination Experiment Constraints on λG at 68%cl WMAP 1.01 ± 0.16 WMAP+POL 0.97 ± 0.13 WMAP+ACBAR 1.03 ± 0.11 PLANCK 1.01 ± 0.015 CVL 1.002 ± 0.004 Table 1 Constraints on λG from current WMAP and ACBAR data and future constraints achievable from the Planck satellite mission and from a cosmic variance limited experiment (CVL). Taken from [10].

CMB data can constrain a constant value of G with an accuracy of ∼ 10% level at 68% c.l., therefore not being competitive with the accuracy quoted by the CODATA commitee of 0.1% at 68% c.l. Only a cosmic variance limited experiment will be able to achieve this precision, reaching an accuracy of ∼ 0.4% Secondly, we have assumed a possible evolution

As mentioned before, non-standard mechanisms could produce extra sources of radiation that could modify the recombination epoch. The processes that lead the recombination of ions into neutral matter are very sensitive to the number of photons that can photonionize, directly or through subsequent excitations, the hydrogen atoms in formation. In particular, an injection of 13.6-eV photons and Lyman-α photons increase the photoionization rate, delaying the redshift at which recombination can take place. An excess of these energetic photons could derive from different kind of sources, as evaporating black holes, annihilating or decaying dark matter, etc., as studied by different authors [22]. Each of these sources could produce these photons at rates that depend on the model chosen to describe them. A first approach to the problem is to suppose that the rate of production of these photons is constant with redshift, as we considered in [11], parameterizing the rate of production of Lyman-α photons with a new parameter εα , and of ionizing

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13.6eV photons with a new parameter εi : dnα dt dni dt

= εα nH H(t)

(2)

= εi nH H(t)

(3)

where nH is the density number of all hydrogen nuclei (free and bound), H(t) is the Hubble parameter, nα is the number density of extra Lyman-α photons and ni of ionizing photons. Figure 1 shows the effect of εα and εi on CMB spectra. The main effect of εα is delaying the recombination redshift, therefore increasing the dimension of the sound horizon at last scattering surface (LSS) and shifting the position of the peaks of the spectra at smaller . On the other hand, εi increases the amount of free electrons that survives after recombination, modifing the EE polarization spectrum even at small . Both εα and εi widen the thickness of the LSS, decreasing the hights of the peaks and enhancing Silk Damping at smaller scales. We have introduced εα and εi in a modified version of the RECFAST routine ([18]) in the CAMB code ([19]), contained in the COSMOMC code ([20]). Table 2 shows the constraints obtained for these parameters using different datasets and using simulated Planck data.

Experiment εα εi WMAP < 0.39 < 0.058 WMAP+ACBAR < 0.31 < 0.053 PLANCK < 0.01 < 0.0005 Table 2 Constraints on εα and εi at 95% obtained using different sets of CMB data. Taken from [11].

The εi parameter is better constrained as an excess of 13.6-eV photons affects temperature and polarization power spectra, in particular modifing the reionization peak in the EE polarization spectrum, that is the part of the spectrum better constrained by current data. On the contrary εα has a small effect on this part of the polar-

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ization spectrum, being therefore less constrained but current data. Our results demonstrate that there is still room to suppose that non standard processes could be present during the formation of the CMB, even if our current constraints are compatible with nodetection as well. Moreover, it is interesting to notice that the introduction of εα and εi in the recombination model change the accuracy at which it is possible to constrain the cosmic parameters. This is due to the degeneracy between the non-standard parameters with some of the standard parameters, such as the Hubble parameter or the scalar spectral index ns ; the uncertitude on the determination of these parameters can be increased in the non-standard model by more than 50%. 3.1. Annihilating Dark Matter One of the mechanisms that could produce extra-Lyman-α and ionizing photons is Dark Matter (DM) annihilation. This kind of processes has recently received particular attention as they could explain the excess of positrons and electrons in cosmic rays measured by different experiments, such as PAMELA [23], ATIC [24] and FERMI [25]. The attempt to explain these features in terms of Dark Matter annihilation has prompted the proliferation of new DM candidates with very large annihilation cross-section. In particular, models that include the so called ’Sommerfeld enhancement’([26]) of the annihilation cross-section (σv) have been proposed. In these models, the efficent exchange of force carriers at low relative particle velocities leads to a velocity-dependent (σv), which behaves roughly as ∝ 1/v for high v, and saturates below a critical vs (typically smaller than the local velocity dispersion, v), that depends on the ratio between the masses of the force carrier and the DM particle. When recombination occurs, around zr ∼ 1000, the relic WIMPs have not yet formed sizable gravitationally bound structures and are cold enough for the Sommerfeld mechanism to produce substantial enhancement of the annihilation crosssection with respect to the thermal value (after kinetic decoupling DM particle temperature evolves adiabatically as T ∝ z 2 , so v(zr )/c ∼ 10−8 , for

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a O(100GeV/c2 ) mass WIMP). The actual enhancement is model-dependent, because different DM models lead to a different behaviour of (σv), but in general we expect that for large enough cross-sections, DM annihilation will significantly modify the recombination history, thus leaving a clear imprint on the angular power spectra of CMB anisotropy and polarization. In particular, the interaction of the shower produced by the annihilation of these particles with the thermal gas has three main effects: i) it ionizes the gas, ii) it induces Ly-α excitation of the Hydrogen and iii) it heats the plasma. The first two modify the evolution of the free electron fraction xe , the third affects the temperature of baryons. The effects on the CMB spectra are shown in Figure 2. The rate of energy release dE dt per unit volume by a relic self-annihilating dark matter particle is given by dE σv (z) = ρ2c c2 Ω2DM (1 + z)6 f dt mχ

(4)

with nDM (z) being the relic DM abundance at a given redshift z, σv is the effective selfannihilation rate and mχ the mass of our dark matter particle, ΩDM is the dark matter density parameter and ρc the critical density of the Universe today; the parameter f indicates the fraction of energy which is absorbed overall by the gas, under the approximation the energy absorption takes place locally. A fraction of this dE/dt then goes to ionization of the gas (χi ), Ly-α excitation (χα ) and heating (χh ), as described in [27]. In [12] we have searched for an imprint of selfannihilating dark matter in current CMB angular power spectra, introducing the annihilation parameter pann in the CAMB code, defined as: pann = f < σv > /mχ

(5)

and then used the COSMOMC code. Table 3 shows the constraints on pann obtained using the five-year data of the WMAP experiment and using simulated data for the Planck experiment and for a hypotetical cosmic variance limited experiment.

Experiment pann 95% c.l. WMAP < 2.4 × 10−6 m3 /s/kg Planck < 1.7 × 10−7 m3 /s/kg CVl < 5.9 × 10−8 m3 /s/kg Table 3 Upper limit on pann from current WMAP observations and future upper limits achievables from the Planck satellite mission and from a cosmic variance limited experiment. Taken from [12].

The results are visualized in fig.3, were we show the region excluded by our analysis in the (σv) vs. mχ plane, corresponding to the 95 % c.l. upper limit on the cross section by combining equation 5 with the constraints on pann in table 3:   pmax ann × = 71.2 σvzmax −1 −6 3 −1 ,26 r 2.0·10 m s kg    mχ 0.5 × 100GeV (6) f denotes the upper limit of the anwhere σvzmax r ,26 nihilation cross section at recombination in units of 10−26 cm3 s−1 . We have adopted in this formula, and in fig.3, a fiducial value f = 0.5 for the coupling between the annihilation products and the gas, following the detailed calculation of DM–induced shower propagation and energy release performed by [28]. We find that the most extreme enhancements are already ruled out by existing CMB data, while enhancements of order 103 –104 with respect to thermal value σv =3×10−26 cm3 /s, required to explain the PAMELA and ATIC data, will be probed over a larger WIMP mass range by Planck. We also note that for small enough mχ , a CMB experiment allows us to probe the region of thermal cross-sections, and that Planck sensitivity will reach it, making it possible perhaps to find hints of particle DM in CMB data. Aknowledgements It is a pleasure to thank my co-authors in the several papers I review: Rachel Bean, Gianfranco Bertone, Fabio Iocco, Alessandro Melchiorri, Joe Silk, George Smoot, Oliver Zahn. I also would

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[l(l+1)/2π]Cl (μ K)

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εi=0 ε i= 0.001 ε i = 0.01 ε i = 0.1 εi=1

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0 −50 −100

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Figure 1. TT, EE, TE angular power spectra (from Top to Bottom) for different values of εα (left) and εi (right). Taken from [11].

like to thank James Bartlett, Francesco De Bernardis and Luca Pagano.

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Figure 2. TT, EE, TE angular power spectra (from Top to Bottom) for different values of pann = [0, 10−6 , 5 × 10−6 , 10−5 ] m3 /s/Kg. Taken from [12] .

Figure 3. Constraints on the self-annihilation cross-section at recombination (σv)zr , assuming the gas–shower coupling parameter f =0.5, see text for details. Regions above the solid (/long dashed/short dashed) thick lines are ruled out by WMAP5 (/Planck forecast/Cosmic Variance limited); the thin dotted and dashed-dotted lines are the predictions of the “Sommerfeld” enhanced self–annihilation cross sections with force carrying bosons of mφ =1GeV/c2 and mφ =90GeV/c2 respectively, see text for details. Notice that these constraints apply to σv at very low temperatures such that it is in saturated Sommerfeld regime, and therefore directly comparable with results from galatic substructures and dwarf galaxies constraints. Taken from [12].

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REFERENCES 1. G. Hinshaw et al. [WMAP Collaboration], [arXiv:0803.0732]. 2. E. Komatsu et al., [arXiv:0803.0547]. 3. C. L. Reichardt et al., [arXiv:0801.1491]. 4. P.J.E. Peebles, Astrophys. J. 153 1 (1968). 5. Ya. B. Zel’dovich, V.G. Kurt, R.A. Sunyaev, Zh. Eksp. Teoret. Fiz 55 278(1968), English translation, Sov. Phys. JETP. 28 146 (1969). 6. S. Seager, D.D. Sasselov, & D. Scott, Astrophys. J. 523 1 (1999), astro-ph/9909275. 7. W. Hu, D. Scott, N. Sugiyama, & M. White, Phys. Rev. D 52 5498 (1998). 8. U. Seljak, N. Sugiyama, M. White, M. Zaldarriagaastro-ph/0306052 9. E. R. Switzer and C. M. Hirata, Phys. Rev. D 77 (2008) 083006 [arXiv:astro-ph/0702143]; C. M. Hirata and E. R. Switzer, Phys. Rev. D 77 (2008) 083007 [arXiv:astro-ph/0702144]. 10. Galli, S., Melchiorri, A., Smoot, G. F., & Zahn, O. 2009,Phys. Rev. D, 80, 2, [arXiv:0905.1808] 11. Galli, S., Bean, R., Melchiorri, A., & Silk, J. 2008, Phys. Rev. D, 78, 063532,[arXiv:0807.1420] 12. Galli, S., Iocco, F., Bertone, G., & Melchiorri, A. 2009, Phys. Rev. D, 80, 2 [arXiv:0905.0003] 13. Dirac, P.A.M., 1937, Nature (London) 139, 323. Dirac, P.A.M., 1938, Proc. Roy. Soc. London A 165, 198. Dirac, P.A.M., 1974, Proc. Roy. Soc. London A 338, 439. Dirac, P.A.M., 1979, Proc. Roy. Soc. London A 365, 19. 14. Uzan, J.-P. 2003, Reviews of Modern Physics, 75, 403 15. P. R. Heyl, P. Chrzanowski, J. Res. Natl. Bur. Std. U.S. 29, 1 (1942). 16. Peter J. Mohr, Barry N. Taylor, Rev. Mod. Phys., 72, 351, 2000. 17. O. Zahn and M. Zaldarriaga, Phys. Rev. D 67 (2003) 063002 [arXiv:astro-ph/0212360]. 18. S. Seager, D. D. Sasselov and D. Scott, Astrophys. J. Suppl. 128, 407 (2000) [arXiv:astroph/9912182]. 19. A. Lewis, A. Challinor and A. Lasenby, As-

20.

21.

22.

23.

24. 25. 26. 27. 28.

trophys. J. 538, 473 (2000) [arXiv:astroph/9911177]. A. Lewis and S. Bridle, Phys. Rev. D 66, 103511 (2002) (Available from http://cosmologist.info.) T. Clifton, J. D. Barrow, R. J. Scherrer, Phys. Rev. D 71, 123526 (2005); A. Liddle, A. Mazumdar, J. D. Barrow Phys. Rev. D 58, 027302 (1998); F. Wu, L. Qiang, X. Wang, X. Chen, arXiv:0903.0384 [astro-ph]; F. Wu, L. Qiang, X. Wang, X. Chen, arXiv:0903.0385 [astro-ph]. P.J.E. Peebles, S. Seager, W. Hu, Astrophys. J. 539 L1 (2000), astro-ph/0004389. P.D. Naselsky, I.D. Novikov MNRAS 334 137 (2002), astro-ph/0112247 A.G. Doroshkevich, I.P. Naselsky, P.D. Naselsky, I.D. Novikov, Astrophys. J. 586 709 (2002), astroph/0208114. S. Sarkar and A. Cooper, Phys. Lett. B., 148, 347 (1983) D. Scott ,M. J. Rees & D. W. Sciama , A & A, 250, 295, (1991) J. Ellis, G. Gelmini , J. Lopez , D. Nanopoulos, & S. Sarkar , Nucl.Phys.B. 373 399 (1992). A. J. Adams J.A., S. Sarkar & D.W. Sciama , MNRAS, 301, 210 (1998) A. G. Doroshkevich and P. D. Naselsky, Phys. Rev. D 65, 123517 (2002) [arXiv:astroph/0201212]. P. D. Naselsky and L. Y. Chiang, Phys. Rev. D 69, 123518 (2004) [arXiv:astroph/0312168]. L. Zhang, X. L. Chen, Y. A. Lei and Z. G. Si, Phys. Rev. D 74, 103519 (2006) [arXiv:astroph/0603425]. O. Adriani et al. [PAMELA Collaboration], Nature 458, 607 (2009) [arXiv:0810.4995 [astro-ph]]. J. Chang et al., Nature 456, 362 (2008). Abdo, A. A., et al. 2009, Physical Review Letters, 102, 181101 M. Lattanzi and J. I. Silk, arXiv:0812.0360 [astro-ph] Shull, J. M.; van Steenberg, M. E. Astrophys. J. 298 268 (1985) D. Finkbeiner, [Private Communication]