MNRAS 452, 2220–2224 (2015) doi:10.1093/mnras/stv1443 Large-scale structure and integrated Sachs–Wolfe effect in decaying vacuum cosmology H. Velten,1,2‹ H. A. Borges,3,4 S. Carneiro,3‹ R. Fazolo1 and S. Gomes1 1Departamento de F´ısica, Universidade Federal do Esp´ırito Santo, 29075-910 Vitoria,´ ES, Brazil 2CPT, Aix Marseille Universite,´ UMR 7332, F-13288 Marseille, France 3Instituto de F´ısica, Universidade Federal da Bahia, 40210-340 Salvador, BA, Brazil 4Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK Accepted 2015 June 26. Received 2015 June 12; in original form 2015 April 17 ABSTRACT The concordance particle creation model – a class of (t) Cold Dark Matter (CDM) cosmolo- gies – is studied using large-scale structure (LSS) formation, with particular attention to the integrated Sachs–Wolfe effect. The evolution of the gravitational potential and the amplitude of the cross-correlation of the cosmic microwave background (CMB) signal with LSS sur- veys are calculated in detail. We properly include in our analysis the peculiarities involving the baryonic dynamics of the (t)CDM model which were not included in previous works. Although both the (t)CDM and the standard cosmology are in agreement with available data for the CMB–LSS correlation, the former presents a slightly higher signal which can be identified with future data. Key words: dark energy – dark matter. ˙ =− 1 INTRODUCTION from which it is not difficult to show that ρm. The back- ground expansion is given by Although the great success of the standard CDM cosmological = − + −3/2 model in describing most observations, we are still distant from H H0 1 m0 m0a , (2) the full understanding of the cosmic dynamics. Apart from the so- from which we can derive the matter density evolution called small-scale problems in the dark matter sector, there is also a = 2 2 −3 + − −3/2 huge discussion about dark energy properties. At the same time, the ρm 3H0 m0a (1 m0)m0a . (3) efficient approach given by a cosmological constant still seems Note that, as in the flat CDM model, there are here also only two to face some challenges, mainly from the theoretical point of view. free parameters. The concordance of this (t) cosmology with Among the viable alternatives, it has been argued that a model m0 ≈ 0.45 has been verified via many different observational data at with the mechanism of dark matter particle production at a constant both the background (Velten, Montiel & Carneiro 2005;Carneiro rate (implying in a dynamical vacuum term (t)) is also capable et al. 2006, 2008; Pigozzo et al. 2011) and perturbative (Zimdahl to produce a concordance model (Alcaniz et al. 2012), although et al. 2011; Alcaniz et al. 2012;Devietal.2015)levels. with a larger current matter fraction ≈ 0.45.1 m0 Concerning structure formation, the full cosmic microwave back- If the total energy is given by ρ = ρ + and the pressure of the m ground (CMB) spectrum has not yet been obtained for this model, vacuum contribution sets to p =−, a constant is equivalent to but CMB physics can also be accessed via integrated Sachs–Wolfe take = 2H,whereH = a/a˙ is the Hubble rate.2 Taking today’s (ISW) studies, i.e. how time-varying gravitational potential wells values one finds = 3 H /2. The matter dynamics corresponds 0 0 change the temperature of the CMB photons as they cross structures to the balance (Sachs et al. 1967). The expansion of an Einstein–de Sitter universe ρ˙m + 3Hρm =−,˙ (1) compensates the clustering of structures, producing no ISW effect, i.e. in a matter dominated universe there is no ‘late time’ ISW effect.3 Dark energy modifies the background expansion and leads to a net contribution to (T/T)ISW. Then, it is expected that the E-mail: [email protected] (HV); [email protected] (SC) 1 = = 2 π modified background and perturbative expansion of the (t)CDM For any component i we define i ρi/ρc0 with ρc0 3H0 /8 G,where the subscript 0 denotes today’s values. In this paper we will take 8πG = model leaves a distinct imprint on the ISW signal. c = 1. 2 Strictly speaking, this equivalence is only valid if we neglect the conserved baryons in the background equations. In the presence of a small baryonic 3 The ‘early time’ ISW effect is related to non-insignificant radiation density content, taking ∝ H does not lead to an exactly constant . just after photon decoupling. C 2015 The Authors Downloaded from https://academic.oup.com/mnras/article-abstract/452/2/2220/1070245/Large-scale-structure-and-integrated-Sachs-WolfePublished by Oxford University Press on behalf of the Royal Astronomical Society by University of Portsmouth Library user on 20 September 2017 LSS and ISW effect in decaying vacuum cosmology 2221 Since the ISW is a secondary CMB temperature effect its de- and the Friedmann equation tection occurs only via the cross-correlation with other large-scale + = probes like galaxies and quasars surveys (Crittenden et al. 2005). 2aHH ρm 0, (7) Wang et al. (2010) used the cross-correlation technique to probe where the prime means derivative with respect to the scale factor. the (t)CDM model, finding an increase of the ISW-galaxy spec- Tg trum (Cl ) in comparison to the CDM model. Our aim in this paper is to perform this analysis taking care with some peculiari- ties of the model. In particular, it is important to differentiate the 3 PERTURBATIVE DYNAMICS evolution of the baryonic and dark matter components. At the back- ground level, baryons are included in the conserved part of equation 3.1 Growth functions (3). Concerning perturbations, the observed matter power spectrum When cosmological perturbation theory is used to study the large- =| |2 P(k) δ(k) is a measurement of the baryonic clustering, which is scale structure (LSS) of the universe we are most interested in the sourced by the gravitational potential. In the CDM model there is evolution of scalar quantities like the density contrast and the grav- almost no difference between the evolution on large scales of such itational potential. The (t)CDM models have the particularity of components. The same does not happen in the (t)CDM model, suppressing the growth of dark matter contrast δdm.However,the where one observes a late-time suppression in the dark matter and observed structures reflect the behaviour of the baryonic contrast, total matter contrasts owing to dark matter production, a suppression δb = δρb/ρb, instead. In the standard cosmology this quantity co- not observed in the baryonic contrast. incides with the dark matter contrast, and the total matter contrast Our interest is also justified by a possible tension between the δm denotes both behaviours. For the (t)CDM model, however, we theoretical CDM predictions and the observed ISW signal. Some should make a distinction between the different components. Using analysis have reported a cross-correlation signal 1σ –2σ above that the fact that the vacuum fluctuations are negligible (Zimdahl et al. expected in the standard cosmology (Giannantonio et al. 2008; Goto, 2011) and choosing the comoving synchronous gauge we obtain the Szapudi & Granett 2012, see Giannantonio et al. 2012 for a critical set of equations4 review on this issue). Recent studies claim a better statistical concor- dance though the observed signal is still higher than the theoretical h˙ δ˙ + δ = , (8) one (Kovacs´ et al. 2013; Ferraro, Sherwin & Spergel 2015). Also, m m 2 the inferred stacking of CMB data on the position of superstruc- ˙ tures is about five times larger than the CDM prediction (Granett, h δ˙b = , (9) Neyrinck & Szapudi 2008; Nadathur, Hotchkiss & Sarkar 2012; 2 Flender, Hotchkiss & Nadathur 2013; Hernandez-Monteagudoet´ & ¨ + ˙ = Smith 2013). This result has recently been confirmed by the 2015 h 2H h ρmδm, (10) release of the Planck CMB data (Planck Collaboration 2015). where h is the trace of the spatial metric perturbation. Combining In the next section we develop the background expansion which these equations and changing to the derivative with respect to the will be used in this paper. In Section 3 we explore the scalar pertur- scale factor we find bations of the model. The connection with the ISW effect is made via a direct calculation of the evolution of the gravitational potential 2 2 + + + a H δm aH(3H aH )δm (Section 3.2) and the ISW–LSS cross-correlation (Section 3.3). We 1 conclude in the final section. + 2Hδ = ρ δ (11) m 2 m m and 1 2 (t) BACKGROUND DYNAMICS a2H 2δ + aH(3H + aH )δ = ρ δ . (12) b b 2 m m The brief description of the (t)CDM dynamics given in equations (1)–(3) has been widely derived in the literature (see Alcaniz et al. In Fig. 1 we plot the evolution of the density contrasts as calculated 2012 and references therein). Note that as in the standard case in equations (11) and (12). For the CDM model (black curves) we set m0 = 0.23, the best fit of LSS observations (Cole et al. 2005; the important quantity is the total matter density m0,thesumof 5 Percival et al. 2007). We show the (t)CDM evolutions for δb and the dark matter dm0 and baryons b0. The latter is constrained δm in the solid red and dashed red curves, respectively. We have by nucleosynthesis and is well approximated by b0 = 0.05. We = = = = −5 assume hereafter this value. The baryonic sector is conserved and used initial conditions δb(a 0.001) δm(a 0.001) 10 and = = = = therefore we have the continuity equations δb(a 0.001) δm(a 0.001) 0.