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

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 $\lambda \mathrm{/}(m{c}^2{)}^2$, 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 $\lambda \mathrm{/}(m{c}^2{)}^2={10}^{-18}$eV${}^{-1}$cm${}^3$, null detection by the aLIGO O1 run excludes 8.7510^3<T_{re} (GeV)<1.710^5 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.