CERN Accelerating science

Landscape of gravitational wave cosmology. Experimental results include: O1-O3 LIGO-Virgo upper limits~\cite{PhysRevD.104.022004}, indirect limits from big bang nucleosynthesis~\cite{PhysRevX.6.011035}, CMB limits~\cite{PhysRevX.6.011035}, and Parkes pulsar timing limit~\cite{PhysRevX.6.011035}, as well as projected sensitivities of the third generation (3G) terrestrial GW detectors~\cite{EinsteinTelescope,CosmicExplorer} and LISA~\cite{LISA}. Theoretical models include examples of slow-roll inflation~\cite{turner}, first-order phase transitions (PT-1~\cite{Ellis:2019oqb}, PT-2~\cite{DelleRose:2019pgi}, and PT-3~\cite{An:2022}), Axion Inflation~\cite{peloso_parviol}, Primordial Black Hole model \cite{Wang:2016ana}, hypothetical stiff equation of state in the early universe~\cite{boylebuonanno}, and foregrounds due to binary black hole/neutron stars~\cite{PhysRevD.104.022004} and galactic binary white dwarfs~\cite{LISA}.

Landscape of gravitational wave cosmology. Experimental results include: O1-O3 LIGO-Virgo upper limits~\cite{PhysRevD.104.022004}, indirect limits from big bang nucleosynthesis~\cite{PhysRevX.6.011035}, CMB limits~\cite{PhysRevX.6.011035}, and NANOGrav pulsar timing measurement~\cite{Arzoumanian_2020}, as well as projected sensitivities of the third generation (3G) terrestrial GW detectors~\cite{EinsteinTelescope,CosmicExplorer} and space-borne LISA~\cite{LISA}, Taiji~\cite{Hu:2017mde}, and Tianqin~\cite{TianQin:2015yph}. Theoretical models include examples of slow-roll inflation~\cite{turner}, first-order phase transitions (PT-1~\cite{Ellis:2019oqb}, PT-2~\cite{DelleRose:2019pgi}, and PT-3~\cite{An:2022}), Axion Inflation~\cite{peloso_parviol}, Primordial Black Hole model \cite{Wang:2016ana}, hypothetical stiff equation of state in the early universe~\cite{boylebuonanno}, and foregrounds due to binary black hole/neutron stars~\cite{PhysRevD.104.022004} and galactic binary white dwarfs~\cite{LISA}.

EWPT strength $\alpha$ versus inverse duration (in Hubble units) $\beta/H^{*}$ for xSM benchmark scenarios. The orange benchmarks feature a singlet mixing $\left|\rm{sin}\,\theta \right| \gtrsim 0.1$, thus within reach of the HL-LHC, while the HL-LHC will not be able to probe the blue points (some of which are within reach of LISA). The red-orange-green curves correspond to the LISA sensitivity with a certain signal-to-noise ratio (indicated in the figure). The black dashed lines correspond to constant values of $(\tau_{\text{sw}} H)^{-1}$ (see section \ref{section_PT}), with $\tau_{\text{sw}} H < 1$ for the grey region. Figure adapted from~\cite{Caprini:2019egz} using \textsc{PTPlot}~\cite{PTPLOT}.

EWPT strength $\alpha$ versus inverse duration (in Hubble units) $\beta/H^{*}$ for xSM benchmark scenarios. The orange benchmarks feature a singlet mixing $\left\vert\rm{sin}\,\theta \right\vert \gtrsim 0.1$, thus within reach of the HL-LHC, while the HL-LHC will not be able to probe the blue points (some of which are within reach of LISA). The red-orange-green curves correspond to the LISA sensitivity with a certain signal-to-noise ratio (indicated in the figure). The black dashed lines correspond to constant values of $(\tau_{\text{sw}} H)^{-1}$ (see section \ref{section_PT}), with $\tau_{\text{sw}} H < 1$ for the grey region. Figure adapted from~\cite{Caprini:2019egz} using \textsc{PTPlot}~\cite{PTPLOT}.

Real triplet extension of the SM. Panel (a) gives the phase diagram in terms of the triplet mass $m_\Sigma$ and Higgs portal coupling $a_2$. The light blue, green, red, and grey areas correspond to singlet step crossover transition, single step first order transition, two step thermal history, and unstable electroweak minimum, respectively. The interior of the black dashed contour corresponds to an EWPT that would complete. The thin black band is the allowed region for a hypothetical LISA observation. The dark (light) ellipses give prospective collider allowed regions for scenarios BMA (BMA'): determination of the triplet mass and Higgs diphoton decay rate (adds a measurement of the neutral triplet decay to two $Z$ bosons). The blue bands in panel (b) show projection of the hypothetical collider allowed parameter space into the plane of GW-relevant inputs. Figures adapted from Ref.~\cite{TripletGW2022}.

Real triplet extension of the SM. Panel (a) gives the phase diagram in terms of the triplet mass $m_\Sigma$ and Higgs portal coupling $a_2$. The light blue, green, red, and grey areas correspond to singlet step crossover transition, single step first order transition, two step thermal history, and unstable electroweak minimum, respectively. The interior of the black dashed contour corresponds to an EWPT that would complete. The thin black band is the allowed region for a hypothetical LISA observation. The dark (light) ellipses give prospective collider allowed regions for scenarios BMA (BMA'): determination of the triplet mass and Higgs diphoton decay rate (adds a measurement of the neutral triplet decay to two $Z$ bosons). The blue bands in panel (b) show projection of the hypothetical collider allowed parameter space into the plane of GW-relevant inputs. Figures adapted from Ref.~\cite{TripletGW2022}.