Matter density perturbation and power spectrum in running vacuum model

Abstract

We investigate the matter density perturbation ${\delta }_m$ and power spectrum $P(k)$ in the running vacuum model (RVM) with the cosmological constant being a function of the Hubble parameter, given by $\Lambda ={\Lambda }_0+6\sigma H{H}_0+3\nu H^2$, in which the linear and quadratic terms of $H$ would originate from the QCD vacuum condensation and cosmological renormalization group, respectively. Taking the dark energy perturbation into consideration, we derive the evolution equation for ${\delta }_m$ and find a specific scale $d_{cr}=2\pi /k_{cr}$, which divides the evolution of the universe into the sub and super-interaction regimes, corresponding to $k\ll k_{cr}$ and $k\gg k_{cr}$, respectively. For the former, the evolution of ${\delta }_m$ has the same behavior as that in the $\Lambda$CDM model, while for the latter, the growth of ${\delta }_m$ is frozen (greatly enhanced) when $\nu +\sigma >(<)0$ due to the couplings between radiation, matter and dark energy. It is clear that the observational data rule out the cases with $\nu <0$ and $\nu +\sigma <0$, while the allowed window for the model parameters is extremely narrow with $\nu ,|\sigma |\lesssim \mathcal{O}(10^{-7})$.

7 pages, 6 figures, revised version accepted for publication in MNRAS

References in corpus (11)

• Dynamics of dark energy
• Cosmologies with Energy Exchange
• Dark Energy and QCD Ghost
• Dynamical vacuum energy in the expanding Universe confronted with observations: a dedicated study
• The $\bar{\Lambda }CDM$ cosmology: from inflation to dark energy through running $\Lambda$
• Vacuum models with a linear and a quadratic term in H: structure formation and number counts analysis
• Gluonic vacuum, q-theory, and the cosmological constant
• Observational constraints on late-time Lambda(t) cosmology
• Evolution of density perturbations in decaying vacuum cosmology
• Evolution of density perturbations in decaying vacuum cosmology: The case of non-zero perturbations in the cosmological term
• Running cosmological constant with observational tests

Cited by in corpus (4)

• Constraints on a special running vacuum model
• Perturbations in the interacting vacuum
• Running vacuum model in non-flat universe
• Observational constraints on running vacuum model