Bose-Einstein-condensed scalar field dark matter and the gravitational wave background from inflation: New cosmological constraints and its detectability by LIGO
Here, we consider an alternative to weakly interacting massive particle (WIMP) cold dark matter (CDM), ultralight bosonic dark matter ($m$ ≳ 10 -22 eV /$c$ 2 ) described by a complex scalar field (SFDM) with a global $U(1)$ symmetry, for which the comoving particle number density, or charge density, is conserved after particle production during standard reheating. We allow for a repulsive self-interaction. In a Λ SFDM universe, SFDM starts relativistic, evolving from stiff ($w$ = 1) to radiation-like ($w$ = 1/3), before becoming nonrelativistic at late times ($w$ = 0). Thus, before the familiar radiation-dominated era, there is an earlier era of stiff-SFDM-domination. During both the stiff-SFDM-dominated and radiation-dominated eras, the expansion rate is higher than in Λ CDM. SFDM particle mass $m$ and quartic self-interaction coupling strength λ, are therefore constrained by cosmological observables, particularly $N$ eff , the effective number of neutrino species during big bang nucleosynthesis, and $z$ eq , the redshift of matter-radiation equality. Furthermore, since the stochastic gravitational wave background (SGWB) from inflation is amplified during the stiff-SFDM-dominated era, it can contribute a radiationlike component large enough to affect these observables, by further boosting the expansion rate after the stiff era ends. Remarkably, this same amplification makes detection of the SGWB possible at high frequencies by current laser interferometer experiments, e.g., aLIGO/Virgo and LISA. For SFDM particle parameters that sat isfy these cosmological constraints, the amplified SGWB is detectable by LIGO for a broad range of reheat temperatures $T$ reheat , for values of the tensor-to-scalar ratio $r$ currently allowed by CMB polarization measurements. For a given $r$ and λ/(mc 2 ) 2 , the marginally allowed Λ SFDM model for each $T$ reheat has the smallest $m$ that satisfies the cosmological constraints and maximizes the present SGWB energy density for that $T$ reheat . This SGWB is then maximally detectable for values of $T$ reheat for which modes that reenter the horizon when reheating ended have frequencies today that lie within the LIGO sensitive band. For example, for the family of marginally allowed models with $r$ = 0.01 and λ/($mc$ 2 ) 2 = 10 -18 eV -1 cm 3 , the maximally detectable Λ SFDM model has $T$ reheat ≃ 2×10 4 GeV and $m$ ≃ 1.6×10 -19 eV/c 2 , for which we predict an aLIGO O1 run detection with signal-to-noise ratio of ~ 10. We show that the null detection of the SGWB recently reported by the aLIGO O1 run excludes the parameter range 8.75 × 10 3 ≲ $T$ reheat (GeV) ≲ 1.7 × 10 5 for this illustrative family at 95% confidence, thereby demonstrating that GW detection experiments can already place a new kind of cosmological constraint on SFDM. A wider range of SFDM parameters and reheat temperatures should be accessible to aLIGO/Virgo O5, with the potential to detect this unique signature of the ΛSFDM model. For this same illustrative family, for example, a 3σ detection is predicted for 600 ≲ $T$ reheat (GeV) ≲ 10 7 .