Single field matter bounce with dark energy era: comparison with CMB Planck 2018 data and best fit parameters

Author(s)

Pinheiro, Rodrigo F., Pinto-Neto, Nelson

Abstract

In this work, we perform Markov Chain Monte Carlo (MCMC) analyses using the Planck 2018 cosmic microwave background (CMB) datasets, including temperature, polarization, and lensing, in order to compare matter bounce models with observational data. The particular model we considered contains a scalar field with an exponential potential, which behaves as dust in the asymptotic past of the contracting phase, it realizes a quantum bounce, and then behaves as a transient dark energy field at large scales in the expanding phase. The parameter $λ$ appearing in the exponential potential is directly related to the model's scalar spectral index, $n_s$, which is set free in the MCMC analyses, as well as the deepness of the bounce, which controls the amplitude of the power spectrum. We provide constraints on the cosmological parameters and compare the model's performance against the standard inflationary $Λ$CDM scenario. Our results indicate that Planck data alone cannot favor one model with respect to the other, showing that the model we investigate can be a viable alternative to inflation.

Figures

The planar system with $\lambda = \sqrt{3}$ and dark energy era in the expanding phase. The system starts at the repeller point $M_{-}$, in the contracting phase ($y < 0$), and ends up at the attractor point $M_{+}$, in the expanding phase ($y>0$). Figure taken from reference \cite{Bacalhau:2017hja}.
Caption The planar system with $\lambda = \sqrt{3}$ and dark energy era in the expanding phase. The system starts at the repeller point $M_{-}$, in the contracting phase ($y < 0$), and ends up at the attractor point $M_{+}$, in the expanding phase ($y>0$). Figure taken from reference \cite{Bacalhau:2017hja}.
The dBB quantum trajectories for $d = -1$ and $\sigma = 1$. The bounce occurs when $\phi = 0$. Figure taken from reference \cite{Bacalhau:2017hja}.
Caption The dBB quantum trajectories for $d = -1$ and $\sigma = 1$. The bounce occurs when $\phi = 0$. Figure taken from reference \cite{Bacalhau:2017hja}.
Time evolution of the Ricci scale for all sets appearing in Table \ref{table:sets}. The parameter d controls how close the scale gets to the Planck length, and set 3 and set 4 are in the limit of validity of our model. Figure taken from reference \cite{Bacalhau:2017hja}.
Caption Time evolution of the Ricci scale for all sets appearing in Table \ref{table:sets}. The parameter d controls how close the scale gets to the Planck length, and set 3 and set 4 are in the limit of validity of our model. Figure taken from reference \cite{Bacalhau:2017hja}.
Constraints on parameters of the $\Lambda$CDM model and bounce models, set 1 and set 2, from the {\it Planck 2018 EE, TE} and {\it TT} high-$\ell$ spectra combined with {\it Planck 2018 TT} and {\it EE} low-$\ell$, and, with {\it Planck 2018 lensing}. Contours contains 68$\%$ and 95$\%$ of the probability.
Caption Constraints on parameters of the $\Lambda$CDM model and bounce models, set 1 and set 2, from the {\it Planck 2018 EE, TE} and {\it TT} high-$\ell$ spectra combined with {\it Planck 2018 TT} and {\it EE} low-$\ell$, and, with {\it Planck 2018 lensing}. Contours contains 68$\%$ and 95$\%$ of the probability.
For the three plots, the top panels shows the TT, TE and EE power spectra, respectively, of the inflationary $\Lambda$CDM model and bounce models, set 1 and set 2, using the best-fit values from the MCMC analyses. In the bottom panels are the TT, TE and EE residuals power spectra of the models with respect to the inflationary $\Lambda$CDM model.
Caption For the three plots, the top panels shows the TT, TE and EE power spectra, respectively, of the inflationary $\Lambda$CDM model and bounce models, set 1 and set 2, using the best-fit values from the MCMC analyses. In the bottom panels are the TT, TE and EE residuals power spectra of the models with respect to the inflationary $\Lambda$CDM model.
For the three plots, the top panels shows the TT, TE and EE power spectra, respectively, of the inflationary $\Lambda$CDM model and bounce models, set 1 and set 2, using the best-fit values from the MCMC analyses. In the bottom panels are the TT, TE and EE residuals power spectra of the models with respect to the inflationary $\Lambda$CDM model.
Caption For the three plots, the top panels shows the TT, TE and EE power spectra, respectively, of the inflationary $\Lambda$CDM model and bounce models, set 1 and set 2, using the best-fit values from the MCMC analyses. In the bottom panels are the TT, TE and EE residuals power spectra of the models with respect to the inflationary $\Lambda$CDM model.
For the three plots, the top panels shows the TT, TE and EE power spectra, respectively, of the inflationary $\Lambda$CDM model and bounce models, set 1 and set 2, using the best-fit values from the MCMC analyses. In the bottom panels are the TT, TE and EE residuals power spectra of the models with respect to the inflationary $\Lambda$CDM model.
Caption For the three plots, the top panels shows the TT, TE and EE power spectra, respectively, of the inflationary $\Lambda$CDM model and bounce models, set 1 and set 2, using the best-fit values from the MCMC analyses. In the bottom panels are the TT, TE and EE residuals power spectra of the models with respect to the inflationary $\Lambda$CDM model.
Primordial power spectrum of the inflationary $\Lambda$CDM model and bounce models, set 1 and set 2, in the best-fit values from the MCMC analyses. The gray band shows the region observed by the Planck satellite.
Caption Primordial power spectrum of the inflationary $\Lambda$CDM model and bounce models, set 1 and set 2, in the best-fit values from the MCMC analyses. The gray band shows the region observed by the Planck satellite.
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