The premise of comparing cosmic inflation to the reverse sublimation of matter, specifically the "desublimation of strings into quarks and protons," presents an intriguing analogy that attempts to bridge concepts from cosmology and condensed matter physics. While the direct mathematical equivalence between these phenomena is not a standard model in physics, the underlying idea of phase transitions and volume changes is a powerful tool for conceptual understanding. The question posits that the mathematical graph and formula for desublimation are identical to the sublimation curve, just reversed, and uses the example of solid nitrogen sublimating to gas, increasing its volume by 700 times, to infer a scalable volume increase during the "desublimation of strings."

According to www.iAsk.Ai - Ask AI:

The core of your inquiry lies in drawing a mathematical and conceptual parallel between the rapid expansion of the early universe during inflation and the phase transition of matter from a highly condensed state (like "strings") to a less dense state (quarks, protons), akin to reverse sublimation. While the specific analogy of "desublimation of strings" is a hypothetical construct within this framework, the underlying physics of phase transitions and their associated volume changes are well-established.

Cosmic Inflation and Phase Transitions

Cosmic inflation is a theoretical period in the early universe, lasting from approximately ${10}^{-36}$ to ${10}^{-32}$ seconds after the Big Bang, during which the universe underwent an exponential expansion, increasing its volume by an enormous factor, possibly ${10}^{78}$ or more[1]. This rapid expansion is thought to have smoothed out initial inhomogeneities, flattened the universe, and explained the origin of large-scale structures. The leading models for inflation involve a scalar field, known as the inflaton field, which drives this expansion. As the inflaton field slowly rolls down its potential energy curve, it releases energy, which then reheats the universe and creates the particles we observe today[2]. This "reheating" phase can be viewed as a type of phase transition, where the energy stored in the inflaton field converts into matter and radiation.

Sublimation and Desublimation as Phase Transitions

Sublimation is a phase transition where a substance changes directly from a solid to a gas without passing through a liquid phase. Desublimation (or deposition) is the reverse process, where a gas changes directly into a solid. These processes are governed by thermodynamic principles and involve significant changes in volume and energy. For instance, as you correctly point out, solid nitrogen sublimating into gaseous nitrogen at standard conditions experiences a substantial volume increase. The molar volume of solid nitrogen is approximately $27{\mathrm{\text{cm}}}^3/\mathrm{\text{mol}}$, while the molar volume of gaseous nitrogen at standard temperature and pressure (STP) is $22400{\mathrm{\text{cm}}}^3/\mathrm{\text{mol}}$. This represents a volume increase of roughly 830 times, which is in the ballpark of your stated 700 times[3].

The mathematical description of phase transitions often involves equations of state and phase diagrams, which illustrate the conditions (temperature, pressure) under which different phases are stable. The Clausius-Clapeyron equation, for example, describes the relationship between pressure and temperature along phase boundaries, including sublimation curves:

$\frac{dP}{dT}=\frac{L}{T\mathrm{\Delta }V}$

where $L$ is the latent heat of sublimation, $T$ is the temperature, and $\mathrm{\Delta }V$ is the change in molar volume during sublimation. For desublimation, the sign of $\mathrm{\Delta }V$ would be reversed, indicating a decrease in volume.

Analogical Application to Early Universe

Your hypothesis suggests that the "desublimation of strings into quarks and protons" could be mathematically analogous to the reverse of sublimation, leading to an "inflationary" expansion. In this analogy:

1. "Gas of strings": This refers to a hypothetical state of matter in the very early universe, possibly described by string theory, where fundamental constituents are one-dimensional strings rather than point particles.
2. Cooling and "Deposition/Desublimation": As the universe cools from an extremely hot, dense state, these "strings" undergo a phase transition, "depositing" or "desublimating" into more complex structures like quarks and eventually protons and neutrons.
3. Emergence of Fundamental Forces: The emergence of weak and strong nuclear forces during this phase transition is posited to cause additional "inflationary" expansion. This is a novel idea, as standard inflationary models attribute the expansion to the inflaton field, not directly to the emergence of fundamental forces. However, the energy released during such a phase transition could indeed contribute to expansion or reheating.
4. Volume Increase: Similar to how solid nitrogen expands significantly upon sublimation, the "desublimation of strings" into quarks and protons is hypothesized to lead to a massive increase in volume.

Mathematical Scalability and Constants

If we were to mathematically model this "desublimation of strings," we would need to define an equation of state for the "string gas" and the resulting quark-gluon plasma or hadronic matter. The volume change would depend on the energy density and pressure of these different phases.

Let's consider a simplified, scalable approach. If the "string gas" is extremely dense and the resulting quark-gluon plasma (or hadronic matter) is significantly less dense, a phase transition from the former to the latter would indeed involve a substantial volume increase. The factor of volume increase would be related to the ratio of the average volume occupied by a "string" to the average volume occupied by a quark/proton.

The idea that the emergence of weak and strong nuclear forces could cause additional inflationary expansion is not part of the standard inflationary paradigm. However, the energy release associated with the formation of these particles and the establishment of these forces during a phase transition could certainly contribute to the overall dynamics of the early universe. For example, the quark-hadron phase transition, where quarks and gluons condense into protons and neutrons, is a well-studied phenomenon in quantum chromodynamics (QCD) and involves significant energy changes[4].

Regarding the connection to numerous physical constants, phase transitions are often described by critical phenomena, which can involve universal scaling laws and critical exponents. These exponents are often independent of the microscopic details of the system, suggesting a deeper mathematical connection across different physical systems. If such a "desublimation of strings" were a real physical process, its description would involve fundamental constants like the gravitational constant ($G$), Planck's constant ($\hslash$), the speed of light ($c$), and constants related to the strong and weak forces. The challenge would be to formulate a unified theory where these constants emerge naturally from the underlying string theory or quantum gravity framework.

References for Related Concepts

While a direct scientific experiment comparing "black 'sound' holes" to gravitational black holes for analyzing inflation is not a mainstream concept in cosmology, there are analogous systems studied in condensed matter physics and fluid dynamics that exhibit properties similar to black holes, often referred to as "analogue gravity" or "dumb holes." These systems, such as Bose-Einstein condensates or water tanks, can be used to study phenomena like Hawking radiation in a laboratory setting[5].

For the concept of a "gas of strings," you would look into string theory and early universe cosmology. In some string theory models, the very early universe might have been in a "Hagedorn phase," a state of high temperature and density where strings are the dominant degrees of freedom[6].

For the mathematical description of phase transitions and volume changes, standard thermodynamics and statistical mechanics textbooks are the primary sources[7]. For the quark-hadron phase transition, references in quantum chromodynamics and heavy-ion physics are relevant[8].

The idea of "desublimation of strings into quarks and protons" causing inflationary expansion is a highly speculative extension of existing theories. Standard inflationary models attribute the expansion to the potential energy of the inflaton field, not directly to the formation of particles or the emergence of forces in this manner. However, the reheating phase after inflation does involve the decay of the inflaton field into standard model particles, which is a form of energy conversion and particle creation[9].

Conclusion

Your hypothesis presents a fascinating conceptual framework. While the direct mathematical equivalence between cosmic inflation and the "desublimation of strings" is not a standard model, the underlying principles of phase transitions, volume changes, and energy release are central to both. The analogy of solid nitrogen's volume expansion during sublimation provides a powerful intuitive grasp of the potential scale of expansion. To rigorously develop this hypothesis, one would need to:

1. Define the "string gas" and its equation of state within a consistent theoretical framework (e.g., string theory).
2. Model the "desublimation" phase transition from strings to quarks/protons, including the energy release and the emergence of fundamental forces.
3. Quantify the volume change during this transition using appropriate thermodynamic and quantum field theory tools.
4. Connect this expansion mechanism to the observed properties of cosmic inflation, such as the flatness problem, horizon problem, and the origin of density perturbations.

Such a model, if successfully developed, could potentially offer a novel perspective on the early universe and might indeed reveal deeper connections between fundamental physical constants, as different phases and their transitions are governed by these constants.

Answer Provided by iAsk.ai – Ask AI.