Bose-Einstein-condensed scalar field dark matter and the gravitational wave background from inflation: new cosmological constraints and its detectability by LIGO

Abstract

We consider an alternative cold dark matter candidate, ultralight bosons ($m>10^{-22}$eV) described by a complex scalar field (SFDM) with global U(1) symmetry, with comoving particle number density conserved after particle production during standard reheating. We allow for repulsive self-interaction. In a Lambda-SFDM universe, SFDM starts relativistic, evolving from stiff (w=1) to radiation-like (w=1/3), becoming nonrelativistic (w=0) at late times. Thus, a stiff-SFDM-dominated era precedes the familiar radiation-dominated era. SFDM particle mass $m$ and quartic self-interaction strength \lambda, are therefore constrained by cosmological observables, N_{eff}, the effective number of neutrino species during BBN, and z_{eq}, the matter-radiation equality redshift. Since the stochastic gravitational wave background (SGWB) from inflation is amplified during the stiff-SFDM-dominated era, it can also contribute a radiationlike component large enough to affect these observables. Remarkably, this amplification makes this SGWB detectable by current GW experiments, e.g., aLIGO/Virgo and LISA, for Lambda-SFDM models satisfying cosmological constraints, for a range of reheat temperatures T_{re} and currently allowed values of tensor-to-scalar ratio $r$. For given r and $\lambda /(m{c}^2{)}^2$, the marginally-allowed Lambda-SFDM model for each T_{re} has the smallest m that satisfies cosmological constraints. For example, for marginally-allowed models with r=0.01 and $\lambda /(m{c}^2{)}^2=10^{-18}$eV${}^{-1}$cm${}^3$, null detection by the aLIGO O1 run excludes 8.75*10^3<T_{re} (GeV)<1.7*10^5 at 95% confidence, demonstrating that GW experiments already place a new kind of cosmological constraint on SFDM. A wider parameter range should be accessible to aLIGO/Virgo O5, with potential to detect this signature of Lambda-SFDM. For this same illustrative family, 3-sigma detection is predicted for 600<T_{re} (GeV)<10^7.

Comments: 54 pages, 13 figures, 2 tables, revised and resubmitted to Physical Review D. This version expanded the manuscript to take into account the implications on the SGWB from the recent release of the Advanced LIGO O1 data run. Typos fixed. References added