High-scale Mirror Standard Model Dark Matter, Dark Phase Transitions and Gravitational Waves Implications

Abstract: We consider a scenario for dark matter in the Universe, according to which the dark matter sector is comprised by a dark Standard Model sector which interacts only gravitationally with the ordinary Standard Model sector. This dark Standard Model sector is assumed to have the same symmetries as the ordinary Standard Model, with the couplings and the scale of the mirror Standard Model sector being different than the ordinary Standard Model sector. Specifically, the scale of the mirror Standard Model sector will be assumed to be quite higher compared to the ordinary Standard Model. Also the Yukawa couplings among the mirror Higgs and the mirror fermions are assumed to be different from those of the Standard Model and we examine the effects of the different scale and of the different Yukawas on the evolution of the Universe. As we show, a mirror world phase transition occurs at high temperatures of the baryonic Universe, which can be first order or second order, depending on the scale of the Universe and the Yukawa couplings. These are dark phase transitions which occur quite earlier than the real world Standard Model electroweak phase transition. The case of a second order phase transition is quite interesting phenomenologically, since it can potentially have a direct imprint on the spectrum of stochastic gravitational waves for frequencies probed by the future gravitational wave detectors. Also we examine whether this mirror dark matter world can form atoms and as we show in some scenario the high scale mirror dark matter can have both atomic and subatomic particle components. We also give an approximation of the total equation of state of high scale mirror DM and we discuss how high scale mirror DM can reconcile contradicting observations like the Bullet cluster and the Abell 520 cluster.

• The paper demonstrates that a high-scale mirror SM extension yields viable dark matter candidates with variations in atomic formation.
• It uses two scenarios with different Yukawa couplings to explore second-order and weak first-order electroweak-like phase transitions, impacting gravitational wave spectra.
• The analysis shows that mirror dark matter properties can resolve small scale structure issues while offering potential gravitational wave signatures for detection.

High-scale Mirror SM Dark Matter, Dark Phase Transitions, and Gravitational Wave Signatures

Introduction and Model Construction

The work "High-scale Mirror Standard Model Dark Matter, Dark Phase Transitions and Gravitational Waves Implications" (2606.14385) investigates an extension of the Standard Model (SM) incorporating a mirror sector with a higher symmetry-breaking scale and disparate Yukawa couplings. In this framework, the mirror sector only interacts gravitationally with the visible sector, resulting in a viable candidate for dark matter (DM) with distinctive cosmological and astrophysical implications.

The central consideration is a Universe described by the gauge group $G\otimes G_M$ with $G_M = SU_M(3)\times SU_M(2)\times U_M(1)$, mirroring the SM but with its own set of couplings and a vacuum expectation value (vev) $v_M \gg v_{SM}$. The mirror sector maintains a lower temperature than the visible sector ($T' < 0.5\,T$) to respect Big Bang nucleosynthesis constraints on extra relativistic species. This scenario enables varied possibilities for DM composition, atomic structure formation, and phase-transition dynamics in the early Universe.

Mirror Sector Abundance and Atomic Structure

The relic abundance and detailed composition of the high-scale mirror sector depend critically on the mirror Higgs self-coupling, Yukawa couplings, and the scale $v_M$. Two regimes are emphasized:

• Scenario I: Yukawa couplings in the mirror sector are much smaller than the SM values, resulting in light mirror fermions but a small fine-structure constant and negligible atomic binding energies. Atomic mirror DM does not form, but the sector still accounts for the majority of the DM density.
• Scenario II: Yukawa couplings are close to the SM, leading to heavier mirror particles and sizable atomic binding energies, permitting early recombination and atomic mirror DM.

The analysis demonstrates that for suitable parameters, the mirror sector may comprise all or a fraction of the DM, with abundance sensitive to the mirror Higgs self-coupling $\lambda_{H'}$ and the sector’s temperature ratio.

Figure 1: Abundance of mirror DM particles versus the mirror Higgs self-coupling $\lambda_{H'}$.

Atomic structure is addressed via the binding energy formula:

$E'_B = \frac{m_{e'}{\alpha'^2}}{2}$

Calculations show that, with low Yukawas in Scenario I, the mirror hydrogen binding energy is sub-eV, inhibiting atom formation. In Scenario II, heavier mirror electrons and a larger $\alpha'$ lead to binding energies $\sim 100$ eV, promoting early and efficient recombination, with possible implications for mirror baryonic structures such as dark atoms and compact objects.

High-Temperature Mirror Electroweak Phase Transitions

The nature of the mirror sector’s electroweak-like phase transition is dictated by the choice of scale and Yukawas:

• Scenario I: Exhibits a second-order phase transition with no potential barrier at the critical temperature ($G_M = SU_M(3)\times SU_M(2)\times U_M(1)$0 GeV), as evident from the form of the finite-temperature effective potential.

Figure 2: Effective potential of the high-scale mirror SM at $G_M = SU_M(3)\times SU_M(2)\times U_M(1)$1 GeV, showing the typical characteristics of a second-order phase transition.

Figure 3: Evolution of the mirror SM effective potential near the critical temperature $G_M = SU_M(3)\times SU_M(2)\times U_M(1)$2, confirming the second-order nature.

• Scenario II: Results in a weak first-order phase transition at intermediate temperatures ($G_M = SU_M(3)\times SU_M(2)\times U_M(1)$3 GeV), as evidenced by the emergence of a barrier and metastable minima in the effective potential.

  Figure 4: High-temperature effective potential in Scenario II for various $G_M = SU_M(3)\times SU_M(2)\times U_M(1)$4 near the critical temperature, showing a first-order transition characteristic.

The order and strength of these transitions have direct consequences for cosmological signatures, notably in gravitational wave backgrounds.

Stochastic Gravitational Wave Signatures

The authors analyze the imprint of dark phase transitions on the stochastic gravitational wave (GW) background, emphasizing that the detectability and spectra are highly sensitive to the transition order and DM abundance.

• Scenario I (Second-order transition):

The rolling of the mirror Higgs significantly modifies the background equation of state (EoS) during the radiation-dominated era. For parameter choices where the entire DM is mirror sector, the transition can substantially deform the stochastic GW spectrum described by

$G_M = SU_M(3)\times SU_M(2)\times U_M(1)$5

with $G_M = SU_M(3)\times SU_M(2)\times U_M(1)$6 determined by the altered EoS. Different values of $G_M = SU_M(3)\times SU_M(2)\times U_M(1)$7 (the effective EoS parameter) correspond to fast or slow rolling of the mirror Higgs field.

Figure 5: $G_M = SU_M(3)\times SU_M(2)\times U_M(1)$8-scaled GW energy spectrum for $G_M = SU_M(3)\times SU_M(2)\times U_M(1)$9 (slow-roll), showing impact in the LISA/BBO/DECIGO frequency range.

Figure 6: GW spectrum for $v_M \gg v_{SM}$0 (fast-roll), with enhanced detectability by BBO.

Figure 7: GW spectrum for $v_M \gg v_{SM}$1, with substantial signal in both DECIGO and BBO sensitivity bands.

• Scenario II (First-order transition):

Despite the presence of a first-order transition and possible bubble nucleation, the analysis reveals that for a high-scale mirror sector, the predicted gravitational wave signal is far too weak for detection in any upcoming GW experiment due to excessively small $v_M \gg v_{SM}$2 and unphysically large $v_M \gg v_{SM}$3.

Mirror DM Equation of State and Astrophysical Implications

The composition of DM in this framework can range from predominantly atomic to a hybrid vector of atomic and collisionless components, affecting the effective EoS,

$v_M \gg v_{SM}$4

and hence the adiabatic sound speed $v_M \gg v_{SM}$5 and the Jeans scale $v_M \gg v_{SM}$6. Notably, even a small residual ionization could significantly raise $v_M \gg v_{SM}$7, modifying structure formation and potentially alleviating the CDM small-scale crisis.

The dual nature—collisionless in low-density environments, collisional where partial ionization occurs—enables the model to naturally reconcile contradictory constraints such as the Bullet Cluster and Abell 520. The presence of atomic DM also allows for dissipative phenomena, possibly leading to dark compact objects or dark disks, broadening the phenomenological landscape for DM.

Conclusion

This work demonstrates that a high-scale mirror SM sector with distinct gauge and Yukawa parameters constitutes a flexible DM paradigm. For appropriate values:

• The mirror sector may account for all or part of the DM density, with or without prolific dark atoms.
• The order of the dark electroweak-like phase transition is tunable; a second-order transition in a DM-dominant mirror sector can imprint a measurable signature on the primordial GW background in the LISA/DECIGO/BBO frequency band. In contrast, first-order transitions in this regime yield undetectable GW signals.
• The effective EoS of the mirror sector allows for a spectrum of behaviors, offering possible simultaneous solutions to astrophysical puzzles requiring both collisionless and collisional DM components.

Future research directions include precise predictions for mixed CDM and mirror DM scenarios and targeted searches for GW signals resulting from early-universe dark sector phase transitions. The analysis underscores the rich phenomenology available in high-scale mirror matter constructions and offers quantitative targets for both gravitational wave and cosmological observations.