Imprints on CMB Angular Power Spectrum Modes from Cosmological Reionization

Tiziana Trombetti, Carlo Burigana

Istituto di Astrofisica Spaziale e Fisica Cosmica di Bologna, Bologna, Italy.

DOI: 10.4236/jmp.2012.312242                

Abstract

The accurate understanding of the ionization history of the Universe plays a fundamental role in modern cosmology. It includes a phase of cosmological reionization after the standard recombination epoch, possibly associated to the early stages of structure and star formation. While the simple “τ-parametrization” of the reionization process and, in particular, of its imprints on the Cosmic Microwave Background (CMB) anisotropy likely represents a sufficiently accurate modelling for the interpretation of current CMB data, a great attention has been recently posed on the accurate computation of the reionization signatures in the CMB for a large variety of astrophysical scenarios and physical processes. The amplitude and shape of the B-mode Angular Power Spectrum (APS) depends, in particular, on the tensortoscalar ratio, r, related to the energy scale of inflation, and on the reionization history, thus an accurate modeling of the reionization process will have implications for the precise determination of r or to set more precise constraints on it through the joint analysis of E and B-mode polarization data available in the next future and from a mission of next generation. In this work we review some classes of astrophysical and phenomenological reionization histories, beyond the simpleτ-parametrization, a present a careful characterization of the imprints introduced in all the CMB APS modes. We have implemented a modified version of CAMB, the Cosmological Boltzmann code for computing the CMB anisotropy APS, to introduce the predicted hydrogen and helium ionization fractions. We compared the results obtained for these models for all the non-vanishing (in the assumed scenarios) modes of the CMB APS. Considering also the limitation from potential residuals of astrophysical foregrounds, we discussed the capability of next data to disentangle between different reionization scenarios in a wide range of tensor-to-scalar ratios.

Keywords

Cosmic Microwave Background Radiation: CMBR Polarization; Reionization; Gravitational Waves; CMBR Polarization

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	P. J. E. Peebles, “Recombination of the Primeval Plasma,” The Astrophysical Journal, Vol. 153, 1968, p. 1. doi:10.1086/149628
[2]	Ya. B. Zel’dovich, V. Kurt AND R. A. Sunyaev, “Recombination of Hydrogen in the Hot Model of the Universe,” Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, Vol. 55, No. 1, 1968, pp. 278-286.
[3]	B. J. T. Jones and R. Wyse, “The Ionisation of the Primeval Plasma at the Time of Recombination,” Astronomy & Astrophysics, Vol. 149, No. 1, 1985, p. 144.
[4]	S. Seager, D. D. Sasselov and D. Scott, “How Exactly Did the Universe Become Neutral?” The Astrophysical Journal Supplement Series, Vol. 128, No. 2, 2000, pp. 407-430, arXiv:astro-ph/9912182. doi:10.1086/313388
[5]	N. A. Zabotin and P. D. Naselsky, “The Neutrino Background in the Early Universe and Temperature Fluctuations in the Cosmic Microwave Radiation,” Soviet Astronomy, Vol. 26, 1982, p. 272.
[6]	E. R. Switzer and C. M. Hirata, “Primordial Helium Recombination. III. Thomson Scattering, Isotope Shifts, and Cumulative Results,” Physical Review D, Vol. 77, No. 8, 2008, 3008, arXiv:astro-ph/0702145. doi:10.1103/PhysRevD.77.083008
[7]	A. A. Starobinsky, “Spectrum of Relict Gravitational Radiation and the Early State of the Universe,” Journal of Experimental and Theoretical Physics Letters, Vol. 30, No. 11, 1979, pp. 682-685.
[8]	L. F. Abbott and M. B. Wise, “Constraints on Generalized Inflationary Cosmologies,” Nuclear Physics B, Vol. 244, No. 2, 1984, pp. 541-548. doi:10.1016/0550-3213(84)90329-8
[9]	A. R. Liddle and D. H. Lyth, “COBE, Gravitational Waves, Inflation and Extended Inflation,” Physics Letters B, Vol. 291, 1992, pp. 391-398, arXiv:astro-ph/9208007. doi:10.1016/0370-2693(92)91393-N
[10]	A. R. Liddle and D. H. Lyth, “The Cold Dark Matter Density Perturbations,” Physics Reports, Vol. 231, No. 1-2, 1993, pp. 1-105, arXiv:astro-ph/9303019. doi:10.1016/0370-1573(93)90114-S
[11]	S. Dodelson, “Modern Cosmology,” Academic Press, San Francisco, 2003.
[12]	D. N. Spergel, et al., “Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology,” The Astrophysical Journal Supplement Series, Vol. 170, No. 2, 2007, p. 377, arXiv:astro-ph/06 03449.
[13]	J. Dunkley, et al., “Five-Year Wilkinson Microwave Anisotropy Probe Observations: Likelihoods and Parameters from the WMAP Data,” The Astrophysical Journal Supplement Series, Vol. 180, No. 2, 2009, pp. 306-329, arXiv: astro-ph/0803.0586.
[14]	E. Komatsu, et al., “Five-Year Wilkinson Microwave Anisotropy Probe Observations: Cosmological Interpretation,” The Astrophysical Journal Supplement Series, Vol. 180, No. 2, 2009, p. 330, arXiv:astro-ph/0803.0547.
[15]	D. Larson, et al., “Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-derived Parameters,” The Astrophysical Journal Supplement Series, Vol. 192, No. 2, 2011, arXiv:as- tro-ph/1001.4635.
[16]	E. Komatsu, et al., “Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation,” The Astrophysical Journal Supplement Series, Vol. 192, No. 2, 2011, arXiv:astro-ph/1001.4538.
[17]	R. Cen, “The Universe Was Reionized Twice,” The Astrophysical Journal, Vol. 591, 2003, pp. 12-37, arXiv: as- tro-ph/0210473.
[18]	B. Ciardi, A. Ferrara and S. M. D. White, “Early Reionization by the First Galaxies,” Monthly Notices of the Royal Astronomical Society, Vol. 344, No. 1, 2003, pp. L7-L11, arXiv:astro-ph/0302451. doi:10.1046/j.1365-8711.2003.06976.x
[19]	A. G. Doroshkevich and P. D. Naselsky, “Ionization History of the Universe as a Test for Superheavy Dark Matter particles,” Physical Review D, Vol. 65, No. 12, 2002, Article ID: 13517, arXiv:astro-ph/0201212.
[20]	A. G. Doroshkevich, I. P. Naselsky, P. D. Naselsky and I. D. Novikov, “Ionization History of the Cosmic Plasma in the Light of the Recent Cosmic Background Imager and Future Planck Data,” The Astrophysical Journal, Vol. 586, No. 2, 2002, p. 709, arXiv:astro-ph/0208114. doi:10.1086/367819
[21]	S. H. Hansen and Z. Haiman, “Do We Need Stars to Reionize the Universe at High Redshifts? Early Reionization by Decaying Heavy Sterile Neutrinos,” The Astrophysical Journal, Vol. 600, No. 1, 2004, pp. 26-31, arXiv: astro-ph/0305126. doi:10.1086/379636
[22]	S. Kasuya, M. Kawasaki and N. Sugiyama, “Partially Ionizing the Universe by Decaying Particles,” Physical Review D, Vol. 69, No. 2, 2004, Article ID: 023512, arXiv: astro-ph/0309434.
[23]	P. J. E. Peebles, S. Seager and W. Hu, “Delayed Recombination,” The Astrophysical Journal, Vol. 539, 2000, pp. L1-L4, arXiv:astro-ph/0004389. doi:10.1086/312831
[24]	L. A. Popa, C. Burigana and N. Mandolesi, “Radiative Effects by High-z UV Radiation Background: Implications for the Future CMB Polarization Measurements,” New Astronomy, Vol. 11, No. 3, 2005, pp. 173-184, arXiv: astro-ph/0506454. doi:10.1016/j.newast.2005.07.003
[25]	J. S. B. Wyithe and R. Cen, “The Extended Star Formation History of the First Generation of Stars and the Reionization of Cosmic Hydrogen,” The Astrophysical Journal, Vol. 659, No. 2, 2007, pp. 890-907. doi:10.1086/511948
[26]	C. Burigana, F. Finelli, R. Salvaterra, L. A. Popa and N. Mandolesi, “On the Cosmological Implications of Next and future CMB Space Experiments,” Recent Research Developments in Astronomy & Astrophysics, Vol. 2, 2004, pp. 59-117.
[27]	R. Schneider, R. Salvaterra, T. R. Choudhury, A. Ferrara, C. Burigana and L. A. Popa, “Detectable Signatures of Cosmic Radiative Feedback,” Monthly Notice of the Royal Astronomical Society, Vol. 384, No. 4, 2008, pp. 1525- 1532, arXiv:0712.0538.
[28]	C. Burigana, L. A. Popa, R. Salvaterra, R. Schneider, C. T. Roy and A. Ferrara, “Cosmic Microwave Background Polarization Constraints on Radiative Feedback,” Monthly Notice of the Royal Astronomical Society, Vol. 385, No. 1, 2008, pp. 404-410, arXiv:0712.1913.
[29]	P. Naselsky and L. Y. Chiang, “Late Reionizations of the Universe and Their Manifestation in the WMAP and Future Planck Data,” Monthly Notice of the Royal Astronomical Society, Vol. 347, No. 3, 2004, pp. 921-936, arXiv: astro-ph/0302085.
[30]	U. Seljak and M. Zaldarriaga, “Signature of Gravity Waves in the Polarization of the Microwave Background,” Physical Review Letters, Vol. 78, No. 11, 1997, pp. 2054-2057, arXiv:astro-ph/9609169. doi:10.1103/PhysRevLett.78.2054
[31]	M. Kamionkowski and A. Kosowsky, “Detectability of Inflationary Gravitational Waves with Microwave Background Polarization,” Physical Review D, Vol. 57, No. 2, 1998, pp. 685-691, arXiv:astro-ph/9705219. doi:10.1103/PhysRevD.57.685
[32]	W. Hu, “Reionization Revisited: Secondary Cosmic Microwave Background Anisotropies and Polarization,” The Astrophysical Journal, Vol. 529, 2000, p. 12, arXiv:as- tro-ph/9907103.
[33]	U. Seljak and C. M. Hirata, “Gravitational Lensing as a Contaminant of the Gravity Wave Signal in the CMB,” Physical Review D, Vol. 69, No. 4, 2004, Article ID: 043005, arXiv:astro-ph/0310163. doi:10.1103/PhysRevD.69.043005
[34]	R. Salvaterra, A. Ferrara and P. Dayal, “Simulating High-Redshift Galaxies,” Monthly Notice of the Royal Astronomical Society, Vol. 414, No. 2, 2011, pp. 847-859, arXiv: astro-ph/1003.3873.
[35]	The Planck Collaboration, “The Scientific Programme of Planck,” ESA-SCI(2005)1, 2005, arXiv:astro-ph/0604069.
[36]	The COrE Collaboration, “COrE (Cosmic Origins Explorer) A White Paper,” 2011, arXiv:astro-ph/1102.2181.
[37]	R. Salvaterra, B. Ciardi, A. Ferrara and C. Baccigalupi, “Reionization History from Coupled Cosmic Microwave Background/21-cm Line Data,” Monthly Notice of the Royal Astronomical Society, Vol. 360, No. 3, 2005, pp. 1063-1068, arXiv:astro-ph/0502419.
[38]	I. T. Iliev, U.-L. Pen, J. R. Bond, G. Mellema and P. R. Shapiro, “The Kinetic Sunyaev-Zel’dovich Effect from Radiative Transfer Simulations of Patchy Reionization,” The Astrophysical Journal, Vol. 660, No. 2, 2007, pp. 933-944, arXiv:astro-ph/0609592. doi:10.1086/513687
[39]	R. A. Sunyaev and Ya. B. Zel’dovich, “The Interaction of Matter and Radiation in the Hot Model of the Universe II,” Astrophysics and Space Science, Vol. 4, No. 3, 1970, pp. 301-316.
[40]	Ya. B. Zel’dovich, A. F. Illarionov and R. A. Sunyaev, “Influence of Energy Release on the Radiation Spectrum in the Hot Model of the Universe,” Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, Vol. 68, 1972, p.1217.
[41]	Ya. B. Zel’dovich and R. A. Sunyaev, “The Interaction of Matter and Radiation in a Hot-Model Universe,” Astrophysics and Space Science, Vol. 4, No. 3, 1969, pp. 301- 316. doi:10.1007/BF00661821
[42]	P. Procopio and C. Burigana, “A Numerical Code for the Solution of the Kompaneets Equation in Cosmological Context,” Astronomy & Astrophysics, Vol. 507, No. 3, 2009, pp. 1243-1256, arXiv:0905.2886. doi:10.1051/0004-6361/200912061
[43]	D. J. Fixsen, E. S. Cheng, J. M. Gales, J. C. Mather, R. A. Shafer and E. L. Wright, “The Cosmic Microwave Background Spectrum from the Full COBE FIRAS Data Set,” The Astrophysical Journal, Vol. 473, No. 2, 1996, pp. 576- 587, arXiv:astro-ph/9605054. doi:10.1086/178173
[44]	J. C. Mather, D. J. Fixsen, R. A. Shafer, C. Mosier and D. T. Wilkinson, “Calibrator Design for the COBE Far-Infrared Absolute Spectrophotometer (FIRAS),” The Astrophysical Journal, Vol. 512, No. 2, 1999, p. 511, arXiv: astro-ph/9810373. doi:10.1086/306805
[45]	X. Fan, et al., “Constraining the Evolution of the Ionizing Background and the Epoch of Reionization with z 6 Quasars. II. A Sample of 19 Quasars,” The Astronomical Journal, Vol. 132, No. 1, 2006, pp. 117-136, arXiv:astro-ph/051 2082.
[46]	S. Gallerani, T. R. Choudhury and A. Ferrara, “Constraining the Reionization History with QSO Absorption spectra,” Monthly Notice of the Royal Astronomical Society, Vol. 370, No. 3, 2006, pp. 1401-1421, arXiv:astro-ph/0512129.
[47]	N. Gnedin and X. Fan, “Cosmic Reionization Redux,” The Astrophysical Journal, Vol. 648, No. 1, 2006, p. 1, arXiv:astro-ph/0603794. doi:10.1086/505790
[48]	T. R. Choudhury and A. Ferrara, “Experimental Constraints on Self-Consistent Reionization Models,” Monthly Notice of the Royal Astronomical Society, Vol. Vol. 361, No. 2, 2005, pp. 577-594, arXiv:astro-ph/0411027.
[49]	T. R. Choudhury and A. Ferrara, “Updating Reionization Scenarios after Recent Data,” Monthly Notice of the Royal Astronomical Society, Vol. 371, No. 1, 2006, pp. L55-L59, arXiv:astro-ph/0603617.
[50]	J. Miralda-Escudé, M. Haehnelt and M. J. Rees, “Reionization of the Inhomogeneous Universe,” The Astrophysical Journal, Vol. 530, No. 1, 2000, p. 1, arXiv:astro-ph/98 12306.
[51]	R. Schneider, R. Salvaterra, A. Ferrara and B. Ciardi, “Constraints on the Initial Mass Function of the First Stars,” Monthly Notice of the Royal Astronomical Society, Vol. 369, No. 2, 2006, pp. 825-834, arXiv:astro-ph/051 0685.
[52]	R. H. Kramer, Z. Haiman and S. P. Oh, “Feedback from Clustered Sources during Reionization,” The Astrophysical Journal, Vol. 649, 2006, pp. 570-578, arXiv:astro-ph/ 0604218. doi:10.1086/506906
[53]	Z. Haiman and G. L. Bryan, “Was Star Formation Suppressed in High-Redshift Minihalos?” The Astrophysical Journal, Vol. 650, 2006, pp. 7-11, arXiv:astro-ph/0603 541.
[54]	M. A. Alvarez, P. R. Shapiro, K. Ahn and I. T. Iliev, “Implications of WMAP 3 Year Data for the Sources of Reionization,” The Astrophysical Journal, Vol. 644, No. 2, 2006, p. L101, arXiv:astro-ph/0604447. doi:10.1086/505644
[55]	N. Gnedin, “Effect of Reionization on Structure Formation in the Universe,” The Astrophysical Journal, Vol. 542, No. 2, 2000, pp. 535-541, arXiv:astro-ph/0002151. doi:10.1086/317042
[56]	WaveMetrics Inc. 2010, Igor Pro (version 6.2).
[57]	A. Lewis, A. Challinor and A. Lasenby, “Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann-Robertson-Walker Models,” The Astrophysical Journal, Vol. 538, No. 2, 2000, pp. 473- 476, arXiv:astro-ph/9911177. doi:10.1086/309179
[58]	U. Seljak and M. Zaldarriaga, “A Line-of-Sight Integration Approach to Cosmic Microwave Background Anisotropies,” The Astrophysical Journal, Vol. 469, 1996, pp. 437-444, arXiv:astro-ph/9603033. doi:10.1086/177793
[59]	T. Trombetti and C. Burigana, “Fitting Ionization Fraction and Electron Temperature Histories for Astrophysical Reionization Models,” Internal Report IASF-BO 589/ 2011.
[60]	L. Knox, “Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments,” Physical Review D, Vol. 52, No. 8, 1995, pp. 4307-4318, arXiv:astro-ph/9504054. doi:10.1103/PhysRevD.52.4307
[61]	L. Page, et al., “Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis,” The Astrophysical Journal Supplement Series, Vol. 170, No. 2, 2007, pp. 335-376, arXiv:astro-ph/0603450. doi:10.1086/513699
[62]	L. Toffolatti, G. F. Argüeso, G. de Zotti, P. Mazzei, A. Franceschini, L. Danese and C. Burigana, “Extragalactic Source Counts and Contributions to the Anisotropies of The Cosmic Microwave Background: Predictions for the Planck Surveyor Mission,” Monthly Notice of the Royal Astronomical Society, Vol. 297, No. 1, 1998, pp. 117-127, arXiv:astro-ph/9711085.
[63]	G. de Zotti, R. Ricci, D. Mesa, L. Silva, P. Mazzotta, L. Toffolatti and J. González-Nuevo, “Predictions for High-Frequency Radio Surveys of Extragalactic Sources,” Astronomy & Astrophysics, Vol. 431, No. 3, 2005, pp. 893- 903, arXiv:astro-ph/0410709.
[64]	M. Tucci and L. Toffolatti, “The Impact of Polarized Extragalactic Radio Sources on the Detection of CMB Anisotropies in Polarization,” Advances in Astronomy, 2012, Article ID: 624987, arXiv:astro-ph/1204.0427.
[65]	P. de Bernardis, M. Bucher, C. Burigana and L. Piccirillo, “B-Pol: Detecting Primordial Gravitational Waves Generated during Inflation,” Experimental Astronomy, Vol. 23, No. 1, 2009, pp. 5-16, arXiv:astro-ph/0808.1881.
[66]	L. A. Popa, C. Burigana and N. Mandolesi, “Cosmological Parameter Determination from Planck and Sloan Digital Sky Survey Data in Cold + Hot Dark Matter Cosmologies,” The Astrophysical Journal, Vol. 558, No. 1, 2001, pp. 10-22, arXiv:astro-ph/0102138. doi:10.1086/322448