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Constraining the Cosmology of the Phantom Brane using Distance Measures

Ujjaini Alam, Satadru Bag, Varun Sahni

TL;DR

The paper analyzes a phantom braneworld cosmology in which phantom-like $w_{ m eff}<-1$ arises without a future big rip and where the brane cosmological constant is dynamically screened. By deriving the normal-branch braneworld evolution and fitting to distance measures from SNe Ia, BAO, and compressed CMB data, the authors show that BAO+SNe allow a relatively large brane parameter $\Omega_\ell$ (roughly 0.13–0.30 at 1$\sigma$) in the absence of CMB, while adding compressed CMB data tightens this to $\lesssim 0.08$ (and $\lesssim 0.04$ with dark radiation). They also find that allowing curvature keeps open the possibility of non-flat geometries and that the inferred Hubble constant shifts toward Planck-like values ($H_0 \sim 70$ km s$^{-1}$ Mpc$^{-1}$) with $w_0$ remaining phantom-like around $-1.1$ to $-1.2$, though a tension between low-$z$ and high-$z$ BAO data persists. The results underscore that phantom braneworlds can fit current background-distance data but require self-consistent perturbation treatment to fully exploit CMB information and assess growth, ISW, and lensing effects.

Abstract

The phantom brane has several important distinctive features: (i) Its equation of state is phantom-like, but there is no future `big rip' singularity, (ii) the effective cosmological constant on the brane is dynamically screened, because of which the expansion rate is {\em smaller} than that in $Λ$CDM at high redshifts. In this paper, we constrain the Phantom braneworld using distance measures such as Type Ia supernovae (SNeIa), Baryon Acoustic Oscillations (BAO), and the compressed Cosmic Microwave Background (CMB) data. We find that the simplest braneworld models provide a good fit to the data. For instance, BAO +SNeIa data can be accommodated by the braneworld for a large region in parameter space $0 < Ω_l < 0.3$ at $1σ$. The Hubble parameter can be as high as $H_0 < 78$ km/s/Mpc, and the effective equation of state at present can show phantom-like behaviour with $w_0 < -1.2$ at $1σ$. We note a correlation between $H_0$ and $w_0$, with higher values of $H_0$ leading to a lower, and more phantom-like, value of $w_0$. Inclusion of CMB data provides tighter constraints $Ω_l < 0.1$. (Here $Ω_l$ encodes the ratio of the five and four dimensional Planck mass.) The Hubble parameter in this case is more tightly constrained to $H_0 < 71$ km/s/Mpc, and the effective equation of state to $w_0 < -1.1$. Interestingly, we find that the universe is allowed be closed or open, with $-0.5 < Ω_κ < 0.5$, even on including the compressed CMB data. There appears to be some tension in the low and high $z$ BAO data which may either be resolved by future data, or act as a pointer to interesting new cosmology.

Constraining the Cosmology of the Phantom Brane using Distance Measures

TL;DR

The paper analyzes a phantom braneworld cosmology in which phantom-like arises without a future big rip and where the brane cosmological constant is dynamically screened. By deriving the normal-branch braneworld evolution and fitting to distance measures from SNe Ia, BAO, and compressed CMB data, the authors show that BAO+SNe allow a relatively large brane parameter (roughly 0.13–0.30 at 1) in the absence of CMB, while adding compressed CMB data tightens this to (and with dark radiation). They also find that allowing curvature keeps open the possibility of non-flat geometries and that the inferred Hubble constant shifts toward Planck-like values ( km s Mpc) with remaining phantom-like around to , though a tension between low- and high- BAO data persists. The results underscore that phantom braneworlds can fit current background-distance data but require self-consistent perturbation treatment to fully exploit CMB information and assess growth, ISW, and lensing effects.

Abstract

The phantom brane has several important distinctive features: (i) Its equation of state is phantom-like, but there is no future `big rip' singularity, (ii) the effective cosmological constant on the brane is dynamically screened, because of which the expansion rate is {\em smaller} than that in CDM at high redshifts. In this paper, we constrain the Phantom braneworld using distance measures such as Type Ia supernovae (SNeIa), Baryon Acoustic Oscillations (BAO), and the compressed Cosmic Microwave Background (CMB) data. We find that the simplest braneworld models provide a good fit to the data. For instance, BAO +SNeIa data can be accommodated by the braneworld for a large region in parameter space at . The Hubble parameter can be as high as km/s/Mpc, and the effective equation of state at present can show phantom-like behaviour with at . We note a correlation between and , with higher values of leading to a lower, and more phantom-like, value of . Inclusion of CMB data provides tighter constraints . (Here encodes the ratio of the five and four dimensional Planck mass.) The Hubble parameter in this case is more tightly constrained to km/s/Mpc, and the effective equation of state to . Interestingly, we find that the universe is allowed be closed or open, with , even on including the compressed CMB data. There appears to be some tension in the low and high BAO data which may either be resolved by future data, or act as a pointer to interesting new cosmology.

Paper Structure

This paper contains 12 sections, 11 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Cosmological Evolution of the Braneworld model
  3. Data and Methodology
  4. Supernova Data
  5. BAO data
  6. CMB data
  7. Results
  8. Low and High $z$ BAO data
  9. Compressed CMB data
  10. Analysis of all datasets
  11. Conclusions
  12. Acknowledgements

Figures (7)

  • Figure 1: The current value of the effective equation of state of dark energy ($w_0$) in the braneworld model (\ref{['eq:hubble0']}) is shown as a function of $\Omega_{\ell}$ ($\Omega_{0m}=0.28$ is assumed). For $\Omega_{\ell} \rightarrow 0$, one recovers $\Lambda$CDM limit.
  • Figure 5: Variation of $r_d$ with $h, \Omega_{0 m}$. The black line represents the Base Model with $\Omega_{0 m} =0.3, \ h=0.7, \ \Omega_{\ell}=\Omega_{\Lambda_b}=0$, the orange line represents the variation of $r_d$ with $\Omega_{0 m}$, and the green line represents the variation of $r_d$ with $h$.
  • Figure 6: $1, 2 \sigma$ confidence levels in the $\Omega_{0 m}-H_0$ (left panel), $\Omega_{0 m}-\Omega_{\ell}$ (middle panel), $w_0-H_0$ (right panel) parameter space for the base Phantom brane with $\Omega_{\kappa}=0, \Omega_{C}=0$, using BAO data. The blue contours represent results for the full BAO data, the red contours for low $z$ galaxy data only, and the green contours for the high $z$ Ly$\alpha$ data only. The high and low $z$ BAO data are discrepant at $2\sigma$. $\Omega_{\ell}=0$ represents $\Lambda$CDM.
  • Figure 7: $1, 2 \sigma$ confidence levels in the $\Omega_{0 m}-H_0$ (left panel), $\Omega_{0 m}-\Omega_{\ell}$ (middle panel), $w_0-H_0$ (right panel) parameter space for the base Phantom brane with $\Omega_{\kappa}=0, \Omega_{C}=0$, using compressed CMB +BAO data. The red contours represent results for the $R$ parameter, blue contours for the ${l}_A$ parameter, and the green contours for $\lbrace l_A, R, z_{\star} \rbrace$. $\Omega_{\ell}=0$ represents $\Lambda$CDM.
  • Figure 8: $1, 2 \sigma$ confidence levels in the $\Omega_{0 m}-H_0$ (left panel), $\Omega_{0 m}-\Omega_{\ell}$ (middle panel), $w_0-H_0$ (right panel) parameter space for the base Phantom brane with $\Omega_{\kappa}=0, \Omega_{C}=0$, using SNe Union2.1 + BAO high and low $z$ data + compressed CMB ${l}_A$ or $\lbrace {l}_A, R, z_{\star} \rbrace$ data. The red contours represent results for just the SNe + BAO data, the blue contours use ${l}_A$ in addition, while the green contours use $\lbrace {l}_A, R, z_{\star} \rbrace$ in addition. $\Omega_{\ell}=0$ represents $\Lambda$CDM.
  • ...and 2 more figures