Planck constraints on the non-flat ΛCDM inflation model

Transcription

1 Planck constraints on the non-flat ΛCDM inflation model 1, Bharat Ratra2, Naoshi Sugiyama 1 1 Nagoya University, 2 Kansas State University arxiv:

2 2/16 Contents IntroducKon Non-flat inflakon model Result Summary inikal power spectrum MCMC analyses

3 3/16 Introduction Planck mission put strong constraint on the cosmological parameters. Flat ΛCDM model is consistent with data. However there are some deviakons. deficit in power of the low-l C l TT data higher σ 8 predickon than weak lensing observakon These deviakons might be a possibility of some extended theories. here we focus on the non-flat model. ESA Planck 2015 results. XIII.

4 4/16 Introduction New results of constraints on the σ 8 also show the tension. le^: Kilo Degree Survey (KiDS) right: Dark Energy Survey (DES) S 8 8 m Hildebrandt+ (2016) DES collaborakon (2017)

5 5/16 Non-flat inflation model The metric with a spakal curvature is ds 2 = Friedmann eq is H 2 = dt 2 + a 2 (t) ȧ a In terms of density parameters, 1= 0 + K0 2 dr 2 1 Kr 2 + r2 (d 2 + sin 2 d 2 ) = 8 G 3 K a 2 K > 0 (closed) K < 0 (open) K = 0 (flat) Here, K0 = K H 2 0 wikipedia

6 6/16 Non-flat inflation model The energy density inhomogeneity power spectrum generated by quantum fluctuakons during an early epoch of inflakon in the spakally non-flat universe is Here, q 2 = k 2 + K P (q) (q 2 4K) 2 q(q 2 K) Ratra & Peebles (1995) Ratra (2017) From Ratra s papers, there is no simple Klt opkon, so n s is no longer a free parameter and replaced by Ω K0 which results in a non-flat ΛCDM inflakon model.

7 7/16 Non-flat inflation model This is a generalizakon of the flat-space scale invariant spectrum. On large scales, the frackonal energy density inhomogeneity power spectrum for the bestfit closed ΛCDM model is suppressed relakve to that of flat ΛCDM model. Open case, q runs from 0 to. Closed case, q/sqrt(k) runs 3, 4, 5,. Ratra & Peebles (1995) Ratra (2017) It takes discrete values because the universe is spakally closed. P (q) (q 2 4K) 2 q(q 2 K)

8 8/16 Result CLASS (class-code.net) To compute the fluctuakons in the CMB. Monte python (montepython.net) Data To analyze data by using the Markov chain Monte Carlo (MCMC) method. Planck 2015: TT, lowp, lensing BAO: 6dF, BOSS (LOWZ and CMASS), SDSS

9 9/16 Result: Planck only We found that non-flat models fit the low-l C l beqer than the flat case. When CMB lensing is included, we found that our non-flat model weakens the tension in the σ 8 Ω m constraint. lower σ 8 values are preferred. The spakal curvature density parameter is constrained as, k = (95.45%, TT + lowp + lensing).

10 10/16 Result: + BAO k = Including the BAO data does somewhat degrade the fit in the low-l region. Including the BAO data also degrades the tension in the σ 8 Ω m constraint. The spakal curvature density parameter is constrained as, ± (95.45%, TT + lowp + lensing + BAO). This case is about 4 σ away from flat.

11 11/16 Result: non-flat XCDM model XCDM model in which dark energy is parameterized in terms of the EoS parameter of a fluid. Here the dark energy fluid pressure and energy density are related via, p X = w 0 X It is a simple parameterizakon of the dynamical dark energy that is relakvely straighrorward to use in a computakon. addikonal parameter w 0

12 12/16 Result: XCDM It does not change the fit in the low-l region significantly. similar to the ΛCDM case. In the σ 8 Ω m contour, there is a region that weaken the tension, lower σ 8. This case is about 3 σ away from flat k = w 0 = ± (95.45%, TT + lowp + lensing + BAO) ± 0.10 (68.27%, TT + lowp + lensing + BAO).

13 13/16 Result: non-flat φcdm model φcdm model is physically consistent dynamical dark energy model." φ is the scalar field with a potenkal V ( )= m 2 P Ratra & Peebles (1988) EquaKons of mokon of the non-flat φcdm model are ȧ a 2 = 8 3m 2 ( + ) P K a 2 = m2 P ȧ a 2 +2 m 2 P m 2 P ( +1) =0

14 14/16 Result: non-flat φcdm model φcdm model is physically consistent dynamical dark energy model." φ is the scalar field with potenkal V ( )= m 2 P Ratra & Peebles (1988)

15 15/16 Result: φcdm Including the BAO data does not improve the fit in the low-l region. similar to non-flat ΛCDM & XCDM cases. The tension is weakened in the σ 8 Ω m contour. more consistent with weak lensing. Ω K and α are constrained as follows. k = ± (95.45%, TT + lowp + lensing + BAO). < (95.45%, TT + lowp + lensing + BAO).

16 16/16 Summary arxiv: We study the non-flat inflakon model which realize a reduced power in the large scale region of the energy density inhomogeneity power spectrum. This model is intereskng and might be useful for the tensions in the current CMB observakon. low-l C l deficit, weak lensing σ 8" We also did addikonal works non-flat XCDM, φcdm models arxiv: arxiv:

17 17/16 Backup

18 18/16 Result

19 19/16 Result: φcdm model φcdm model is physically consistent dynamical dark energy model. an analogy with the inflakon. Because there are two big problems in the ΛCDM. cosmological coincidence problem. cosmological constant problem. Velten+ (2014) Weinberg (1989) 0 m0 O(1) GeV 4 Also, recent works (in flat case!): Solà+ (2017), Zhang+ (2017) in which they claim the φcdm is more favored than ΛCDM.