Cosmic Horizon: Insights into Light's Journey and Observational Limits

Soumendra Nath Thakur
0000-0003-1871-7803
12-05-2024

The speed of light in gravitationally bound systems defines the maximum distance between the source and reception of light. However, this limit doesn't necessarily dictate the maximum distance we can observe, as light from far away can still reach us. The concept of a maximum distance due to the speed of light may be unclear, as we can observe objects beyond the distance created by the speed of light. The particle horizon represents the maximum distance light could have reached us since the beginning of the universe, which changes over time as the universe expands.

The particle horizon, also known as the cosmic light horizon, is the maximum distance light emitted by particles could reach an observer over the universe's age. It represents the conformal time, the time it would take for a photon to travel from our location to the farthest observable point, assuming the universe's expansion ceases. Although it lacks physical significance, the particle horizon holds conceptual importance as a measure of distance, as it moves farther away as time elapses and conformal time increases. The proper distance at any given time is equal to the comoving distance multiplied by the scale factor.

Gravity dominates over vast distances, however, photon's diminishing energy becomes accountable, as photon travels out of a gravitational well, but beyond the gravitational influence over vast distances the lengthening of photon's wavelength becomes another consideration due to the expansion of cosmic distance.

Though gravity dominates over vast distances but the attractive force, called gravity, does not extend beyond zero gravity spheres of galactic clusters. The Newton's Law of Universal Gravitation conveys that the force of gravity on one mass due to another mass depends on their separation r according to the dependence 1/r². This also conveys the fact that when the distance between two objects increases, the force of gravity decreases, where r = distance (d).

Therefore photons diminishing its energy as it travels out of a gravitational well. The applicable mathemetical relationship expressed as (E = hΔf). Beyond the gravitational influence over vast distances, the photons continue in lengthening its wavelength within the cosmic expansion. Beyond a threshold distance, which is much more distant than gravitational influence and the influence of the the cosmic expansion combined, photon frequency reaching beyond the detectable radio frequency. The applicable mathemetical relationship expressed as λ ∝ 1/f where λ → ∞, f → 0.

The Doppler's redshift of photons (presented as z=v/c, specifically fʀᴇᴄᴇɪᴠᴇᴅ=√{(c-v)/(c+v)}*fꜱᴏᴜʀᴄᴇ) apply everywhere, it applies to the spatial distance as a result of motion, {presented at  d=cΔt, since, T(λ)received/T(λ)source = ± t(λ)source}. 

Where, in the absence of gravitational effects (absence of inertial mass) photons have no gravitational redshift; also known as Einstein's redshift. Beyond the sphere gravitational influence of galactic or galaxy clusters, especially in intergalactic space, dark energy rules and results in cosmic redshift. The redshift of photons collectively is called Doppler redshift, irrespective of the gravitational and cosmic redshifts. This can be determined as a whole.

The Doppler redshift of photon, due to the collective reasons, is the photon's wavelength (λ) within reasonable redshift value, but beyond a threshold distance, when the photons are nolonger able to travel at c or maintain a reasonable wavelength, photon's detection becomes impossible. As per the mathemetical interpretation the equation c = λf determines photons constant speed. 

Determining Doppler's redshift by using the Doppler formula, when λ ∝ 1/f, λ in detectable range, c = constant, this should calculate a consistent distance commensurate to the change in wavelength between reception and source and the elapsed time in between. Beyond this threshold, when λ is absurdly high and the f is absurdly low, the relationship λ ∝ 1/f where  λ → ∞, f → 0, and so c ≠,< fλ, the constancy of c is broken, photon frequency reaching beyond the detectable radio frequency, and so the photon can no longer travel either at c or detectable wavelength λ, and so the detection of photons beyond a threshold distance becomes impossible. Therefore, the limit of our visible distance is more when the photon is no longer able to travel at c, or λ → ∞ or, f → 0, than a signal travelling faster than light. 

#visibledistance #dopplerredshift #gravitationalredshift #cosmicredshift