Cosmological scalar fields that mimic the $\Lambda CDM$ cosmological model

TL;DR

This paper investigates scalar field models that replicate the standard $ ext{Lambda CDM}$ cosmology's large-scale geometry, analyzing their solutions, behaviors, and implications for cosmological parameter determination.

Contribution

It provides exact analytic solutions for scalar field models mimicking $ ext{Lambda CDM}$ and discusses degeneracies affecting parameter estimation.

Findings

Scalar field models can exactly mimic $ ext{Lambda CDM}$ geometry.

Some models exhibit infinite or singular behavior at finite redshifts.

Degeneracy in scalar field models reduces the precision of $ ext{Omega}_m$ determination.

Abstract

We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard $\Lambda CDM$ cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble parameter (i.e. photometric distance and angular diameter distance as functions on $z$). Asymptotic behavior of the field solutions is studied in the case of spatially flat Universe with pressureless matter and separable scalar field Lagrangians (power-law kinetic term + power-law potential). Exact analytic solutions are found in some special cases. A number of models have the field solutions with infinite behavior in the past or even singular behavior at finite redshifts. We point out that introduction of the cosmological scalar field involves some degeneracy leading to lower precision in determination of $\Omega_m$. To remove this degeneracy additional information is needed beyond the data on large-scale geometry.