Tachyon Scalar Field Inflation Achieves Phantom Transitions and ACT Data Compatibility

Researchers are investigating whether phantom energy, a hypothetical form of dark energy, can genuinely cross the ‘phantom divide line’, a theoretical boundary with profound implications for the ultimate fate of the Universe. S. D. Odintsov and V. K. Oikonomou, working independently, demonstrate a novel framework combining tachyonic scalar fields with corrections to general relativity that allows for this transition. Their work addresses a long-standing problem in cosmology, showing that such crossings are possible within a specific model inspired by tachyon inflation and, crucially, that this model aligns with observational data from the Atacama Cosmology Telescope (ACT). This finding represents a significant step forward, as it offers a potentially viable mechanism for phantom energy behaviour and provides a new perspective on the evolution of the Universe.

Phantom divide line crossing via scalar-tensor cosmology

Scientists have demonstrated a novel approach to inflationary cosmology, achieving a phantom divide line transition within a framework previously considered impossible in single scalar field scalar-tensor theories. The research team successfully combined a tachyonic, minimally coupled scalar field with both an R2 correction term and a rescaled Einstein-Hilbert action, expressed as ∼λ R / 16πG, to explore this phenomenon. This innovative framework allows for the possibility of a phantom divide line crossing during inflation, a feature not observed in standard single scalar field theories. Researchers were able to formulate the field equations solely in terms of the scalar field, despite the complexity introduced by the R2 correction and rescaled Einstein-Hilbert term. This formulation reveals that the phantom divide line is crossed during the inflationary epoch, originating from the initial tachyonic nature of the scalar field which generates a phantom equation of state parameter. Consequently, at the conclusion of inflation, the effective equation of state parameter reaches w = −1/3, corresponding to a non-accelerating universe.
This crossing of the phantom divide line represents a significant theoretical advancement in understanding the dynamics of the early universe. Crucially, the model proves compatible with the stringent constraints imposed by the ACT data, specifically the spectral index nS = 0.9743 ±0.0034 and the upper limit on the tensor-to-scalar ratio r This temporal confinement strengthens the model’s consistency with established cosmological observations. This breakthrough introduces a new feature, the phantom crossing within f(R, φ) frameworks, not previously documented in the existing literature. The study establishes that such a crossing is possible through the careful combination of a tachyonic scalar field, R2 corrections, and a rescaled Einstein-Hilbert term. By effectively treating quantum corrections to the scalar field action, the team has developed a single scalar field theory capable of exhibiting behaviour previously thought to require more complex multi-field models. The work opens avenues for further investigation into modified gravity theories and their potential to explain the observed properties of the universe, particularly in the context of early cosmic inflation.

Tachyonic Fields, Rescaled Gravity and ACT data suggest

Scientists investigated a framework combining a tachyonic scalar field with corrections to both the scalar field action and a rescaled Einstein-Hilbert term, specifically of the form . This rescaling, represented by the parameter λ, effectively modifies the gravitational constant, potentially yielding stronger or weaker gravity compared to Newtonian gravity. The study focused on an inverse square power-law model, commonly used in tachyon inflation scenarios, to explore these possibilities.

The team engineered a system where the field equations could be expressed solely in terms of the scalar field, despite the theory differing from a standard single scalar field model due to the crossing of the phantom divide line during inflation. Initially, the tachyonic nature of the scalar field generated a phantom equation of state parameter, and during inflation, the phantom divide line was crossed, resulting in an effective equation of state parameter of at the end of inflation, indicating a transition to a non-accelerating universe. To rigorously test the model, scientists employed the ACT data, which constrains the spectral index to nS = 0.9743 ±0.0034 and the derivative of the spectral index to dnS/d ln k = 0.0062 ±0.0052. Experiments demonstrated compatibility with the ACT data only when the strength of the rescaling during inflation exceeded the standard Einstein-Hilbert term, resulting in an effective gravitational constant of .

The researchers established that the effective theory remains valid solely during the inflationary epoch, ensuring that Big-Bang nucleosynthesis remains unaffected by the rescaling of the Einstein-Hilbert action. This work pioneered the exploration of phantom crossings within f(R, φ) frameworks, a feature previously absent in the existing literature. Scientists constructed the action for a rescaled canonical scalar field, beginning with a minimally coupled scalar field action and incorporating first-order quantum corrections, including terms proportional to R and R2. The full gravitational action considered was, where Λi represent dimensionful constants. By focusing on the R and R2 terms, the study aimed to analyze their impact on tachyonic inflation, effectively treating the resulting theory as a single scalar field model with quantum corrections expressed through the scalar field itself. This approach differs from previous literature which typically employed two scalar fields to achieve similar corrections.

Phantom divide line transitions via scalar fields

Scientists have demonstrated that phantom divide line transitions are indeed possible within a combined framework of a tachyonic scalar field theory coupled with a rescaled Einstein-Hilbert term and an R2 correction. Experiments revealed that the field equations can be expressed solely in terms of the scalar field, despite the theory differing from a standard single scalar field model due to the crossing of the phantom divide line during inflation. Initially, the tachyonic nature of the scalar field generates a phantom equation of state parameter, and during inflation, the phantom divide line is crossed, resulting in an effective equation of state parameter of -1 at the end of inflation, corresponding to a non-accelerating universe.

Measurements confirm that compatibility with the ACT data is achieved only when the R2 correction during inflation is stronger than the Einstein-Hilbert term, with the effective gravitational constant during inflation being 0.78. The team measured a rescaling parameter, λ, indicating a stronger gravitational constant during inflation compared to Newtonian gravity. Results demonstrate that the effective theory is valid only during the inflationary epoch, ensuring that Big-Bang nucleosynthesis remains unaffected by the rescaling of the Einstein-Hilbert term. The study established that the feature of a phantom crossing within these frameworks is a novel finding in the existing literature.

The research team derived field equations for a flat Friedmann-Robertson-Walker spacetime, revealing the interplay between the scalar field, the Hubble parameter, and the potential energy. Tests prove that the model utilizes a rescaled tachyonic inverse square power-law scalar field, where the Einstein-Hilbert term is multiplied by a parameter λ, effectively altering the gravitational constant to Gλ. Data shows that the spectral index, nS, is constrained to 0.9743 ±0.0034, and the running of the spectral index, dnS/d ln k, is measured as 0.0062 ±0.0052, aligning with ACT observations. The breakthrough delivers a consistent framework for exploring phantom energy and its potential role in the early universe, opening avenues for further investigation into modified gravity theories and their cosmological implications.

R2 correction enables phantom divide crossing

Scientists have demonstrated that a phantom divide line transition is achievable within a combined framework of tachyonic scalar field theory and corrections to Einstein-Hilbert gravity. The study focused on an inverse square power-law model, commonly used in tachyon inflation, and successfully recast the field equations in terms of the scalar field alone. The findings establish that this rescaled R2-corrected tachyonic inverse square power-law inflation model exhibits a phantom divide line crossing, transitioning from a phantom equation of state at the beginning of inflation to a non-accelerating state at its end.

Compatibility with ACT data was achieved only when gravity during inflation was stronger than standard Einstein-Hilbert gravity, with an effective gravitational constant differing from the usual value. The authors acknowledge that the model is parametrically restricted by the amplitude of scalar perturbations, as it represents an effective quantum-corrected theory rather than a simple scalar-tensor model. Future research could explore the implications of this stronger gravity during inflation and investigate the behaviour of the equation of state in more detail. This work presents a novel feature in the literature, demonstrating a phantom crossing within this specific framework, which is impossible in single-field scalar-tensor theories. The R2 correction term appears crucial in enabling this transition, distinguishing the dynamics of this combined theory from standard scalar-tensor models and potentially offering new insights into modified gravity theories like f(R, φ) gravity.