Examining a new form of non-standard dark matter using DESI DR2 data

1. Problem Statement

The standard cosmological model ($\Lambda$CDM) assumes Cold Dark Matter (CDM) with an equation of state (EoS) parameter $w_{dm} = 0$. However, recent observational tensions, particularly the preference for dynamical dark energy (DDE) with an EoS crossing the phantom divide ($w < -1$) found in the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) combined with CMB and Supernova data, suggest potential deviations from standard models.

• The Tension: Standard DDE models (like $w_0w_a$CDM) that fit DESI data often require $w < -1$, which violates the Null Energy Condition (NEC).
• The Alternative: Some researchers propose Non-Standard Dark Matter (NSDM) to alleviate these tensions without violating the NEC. However, previous NSDM models have faced issues:
  • Some have discontinuous EoS parameters.
  • Others use constant non-zero EoS parameters that contradict CMB constraints (which require DM to behave like CDM in the early universe, i.e., $w_{dm} \to 0$ as $a \to 0$).
• Goal: The authors propose a new NSDM model with a continuous EoS that naturally satisfies early-universe CDM constraints and investigate its viability using the latest DESI DR2 data.

2. Methodology

A. Theoretical Model: NSDM Parameterization

The authors introduce a new parameterization for the Dark Matter EoS, $w_{dm}(a)$, based on the physical requirement that DM must behave as CDM ($w_{dm}=0$) and have a vanishing derivative ($dw_{dm}/da = 0$) as the scale factor $a \to 0$.

• Taylor Expansion: Expanding around $a=0$ and retaining the first non-zero term yields:
  $$w_{dm}(a) = w_2 a^2$$
  Here, $w_2$ is the single free parameter. This ensures $w_{dm} \to 0$ smoothly at high redshifts.

B. Cosmological Framework

The study extends three standard models by replacing CDM with this NSDM:

1. $\Lambda w_2$DM: $\Lambda$CDM + NSDM ($w_{de} = -1$).
2. $w w_2$DM: $w$CDM + NSDM ($w_{de} = w$, constant).
3. $w_0 w_a w_2$DM: $w_0w_a$CDM + NSDM ($w_{de} = w_0 + w_a(1-a)$).

The evolution of the Hubble parameter $H(a)$ is calculated using the Friedmann equations, where the NSDM density evolves according to the derived $w_{dm}(a)$.

C. Data Sets

The analysis utilizes a comprehensive combination of cosmological probes:

• CMB: Planck2018 distance priors (shift parameter $R$, acoustic scale $\theta_*$, baryon density $\omega_b$).
• BAO: DESI DR2 measurements covering $0.1 < z < 4.2$ (7 redshift bins).
• Type Ia Supernovae (SN Ia): Three independent compilations:
  • DESY5 (Dark Energy Survey Year 5)
  • Union3
  • PantheonPlus (PP)

D. Statistical Analysis

• Method: Markov Chain Monte Carlo (MCMC) simulations using emcee and GetDist.
• Priors: Flat priors on all parameters.
• Comparison: Models are compared against $\Lambda$CDM using $\Delta \chi^2_{min}$ and statistical significance ($N_\sigma$).
• NEC Violation Check: The probability of violating the NEC ($w < -1$ for DE, or phantom crossing) is quantified by integrating the posterior distributions of relevant parameters ($w$ or crossing scale factor $a_{cross}$).

3. Key Results

A. Constraints on the NSDM Parameter ($w_2$)

The fitting results for the parameter $w_2$ (which dictates the deviation from CDM) show a preference for negative values (implying exotic, DE-like properties at low redshifts):

• $\Lambda w_2$DM: $w_2$ is constrained to be negative at 2.0$\sigma$ – 2.3$\sigma$ confidence levels (CL) across all data combinations.
• $w w_2$DM: The preference for negative $w_2$ is stronger, reaching 2.4$\sigma$ – 3.3$\sigma$ CL. The correlation between $w$ (DE EoS) and $w_2$ enhances this deviation.
• $w_0 w_a w_2$DM: The preference for non-zero $w_2$ is weaker (below 2$\sigma$), suggesting that the CPL DE sector absorbs some of the non-cold behavior.

B. Alleviating Null Energy Condition (NEC) Violations

A major finding is that introducing NSDM significantly reduces the probability of violating the NEC in models that otherwise favor phantom dark energy ($w < -1$):

• In $w$CDM vs. $w w_2$DM:
  • Standard $w$CDM shows a tendency to violate NEC (significance up to 0.6$\sigma$ for $w < -1$).
  • Replacing CDM with NSDM ($w w_2$DM) shifts the distribution such that the probability of $w < -1$ drops significantly (significance levels become negative, e.g., $-3.5\sigma$), meaning the violation is highly disfavored.
• In $w_0w_a$CDM vs. $w_0 w_a w_2$DM:
  • Standard $w_0w_a$CDM shows a strong preference for phantom crossing ($a_{cross} \in (0,1)$) with significance up to 4.5$\sigma$.
  • The $w_0 w_a w_2$DM model reduces this significance to 1.2$\sigma$ – 2.2$\sigma$, effectively mitigating the need for NEC violation to fit the data.

C. Model Comparison ($\Delta \chi^2$)

The authors compare the goodness-of-fit of the new models against $\Lambda$CDM:

• $w w_2$DM: Preferred over $\Lambda$CDM with significance ranging from 1.7$\sigma$ to 3.5$\sigma$.
• $w_0 w_a w_2$DM: Preferred over $\Lambda$CDM with significance ranging from 1.8$\sigma$ to 3.6$\sigma$.
• Comparison to $w_0w_a$CDM: The statistical significance of the NSDM models is comparable to that of the standard dynamical DE model ($w_0w_a$CDM), which is favored at 2.0$\sigma$–3.7$\sigma$.

4. Significance and Conclusions

1. Viable NSDM Candidate: The proposed $w_{dm} = w_2 a^2$ model is a physically motivated, continuous EoS parameterization that respects early-universe CDM constraints while allowing for non-cold behavior at late times.
2. Alternative to Phantom Dark Energy: The study demonstrates that the "phantom" behavior (NEC violation) often required by DESI DR2 data to fit the expansion history can be explained instead by Non-Standard Dark Matter.
3. Theoretical Consistency: By replacing CDM with NSDM in dynamical DE models, the authors show that the universe can fit the latest observational data without violating fundamental energy conditions (NEC), offering a more theoretically robust solution to the DESI anomaly.
4. Data Preference: Current data (CMB + DESI + SN Ia) mildly to moderately favors these NSDM extensions over standard $\Lambda$CDM, with statistical significance comparable to the widely studied $w_0w_a$CDM model.

In summary, this work provides a compelling alternative interpretation of recent cosmological tensions, suggesting that the observed dynamics may stem from the intrinsic properties of Dark Matter rather than exotic Dark Energy.