user5866: How are the elements of Buddhist Cosmology (31 planes of existence, hungry ghosts/shades, angry deities, etc.) confirmed? 
Are there writings of recent gurus in the past 50 years or so, confirming, questioning or analyzing the elements of this cosmology in the light of modern science and their own experience?
Other than faith in the ancient texts, is there any other basis for modern Buddhists to believe in Buddhist Cosmology? If so, what is that basis?

user5513:  How are the elements of Buddhist Cosmology (31 planes of existence, hungry
 ghosts/shades, angry deities, etc.) confirmed? 

There are those that are born natural Mediums. Their ability to detect outside the normal human frequency, like many animals, is heightened. Their E.S.P., or extra sensory perception, extends beyond the normal physical senses. They simply are able to tune into a frequency band greater than most. Some can see ghosts; some can only hear them, while other Mediums are shown visions and guidance in their mind's eye, or "third eye" from the beyond. These are the John Edwards of the world, or the crime solving specialists..... 
Are there writings of recent gurus in the past 50 years or so, confirming,
questioning or analyzing the elements of this cosmology in the light of modern
science and their own experience?

Refer Edgar Cayce.

    Other than faith in the ancient texts, is there any other basis for modern
Buddhists to believe in Buddhist Cosmology? If so, what is that basis?

parallel universes.
The multiverse (or meta-universe) is the hypothetical set of infinite or finite possible universes (including the Universe we consistently experience) that together comprise everything that exists: the entirety of space, time, matter, and energy as well as the physical laws and constants that describe them. The various universes within the multiverse are also called "parallel universes" or "alternate universes".
The structure of the multiverse, the nature of each universe within it and the relationships among the various constituent universes, depend on the specific multiverse hypothesis considered. Multiple universes have been hypothesized in cosmology, physics, astronomy, religion, philosophy, transpersonal psychology, and fiction, particularly in science fiction and fantasy. In these contexts, parallel universes are also called "alternate universes", "quantum universes", "interpenetrating dimensions", "parallel dimensions", "parallel worlds", "alternate realities", "alternate timelines", and "dimensional planes", among other names.

user43: Buddha's response to such questions has been that whether or not other worlds exist, his teaching is still beneficial if applied in practice.
So, for example, if it is said that acting on an extreme negativity-rooted-in-confusion leads to hell, whether the hell is taken literally as a place you go to or metaphorically as a highly disagreeable state of subjective experience, in either case it is something a sane person would definitely prefer to avoid, and so refraining from acting out one's negativity rooted in confusion should be beneficial in either case.
While I personally lean towards a more "secular" view, I feel that by shifting my focus from the metaphysics ("how things are") and towards soteriological methodology ("how to act towards Bodhi") I can avoid hurtful and non-productive arguments in the public space.

5866: <p>How are the elements of Buddhist Cosmology (31 planes of existence, hungry ghosts/shades, angry deities, etc.) confirmed? </p>

<p>Are there writings of recent gurus in the past 50 years or so, confirming, questioning or analyzing the elements of this cosmology in the light of modern science and their own experience?</p>

<p>Other than faith in the ancient texts, is there any other basis for modern Buddhists to believe in Buddhist Cosmology? If so, what is that basis?</p>
 5513: <pre><code> How are the elements of Buddhist Cosmology (31 planes of existence, hungry
 ghosts/shades, angry deities, etc.) confirmed? 
</code></pre>

<p>There are those that are born natural Mediums. Their ability to detect outside the normal human frequency, like many animals, is heightened. Their E.S.P., or extra sensory perception, extends beyond the normal physical senses. They simply are able to tune into a frequency band greater than most. Some can see ghosts; some can only hear them, while other Mediums are shown visions and guidance in their mind's eye, or "third eye" from the beyond. These are the John Edwards of the world, or the crime solving specialists..... </p>

<pre><code>Are there writings of recent gurus in the past 50 years or so, confirming,
questioning or analyzing the elements of this cosmology in the light of modern
science and their own experience?
</code></pre>

<p>Refer <a href="http://www.edgarcayce.org/are/edgarcayce.aspx?id=1036" rel="nofollow noreferrer">Edgar Cayce</a>.
<a href="https://i.stack.imgur.com/YO049.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/YO049.png" alt="http://www.edgarcayce.org/search.aspx?searchtext=cosmology"></a></p>

<pre><code>    Other than faith in the ancient texts, is there any other basis for modern
Buddhists to believe in Buddhist Cosmology? If so, what is that basis?
</code></pre>

<h2>parallel universes.</h2>

<p><a href="https://en.wikipedia.org/wiki/Multiverse" rel="nofollow noreferrer">The multiverse</a> (or meta-universe) is the hypothetical set of infinite or finite possible universes (including the Universe we consistently experience) that together comprise everything that exists: the entirety of space, time, matter, and energy as well as the physical laws and constants that describe them. The various universes within the multiverse are also called "parallel universes" or "alternate universes".</p>

<p>The structure of the multiverse, the nature of each universe within it and the relationships among the various constituent universes, depend on the specific multiverse hypothesis considered. Multiple universes have been hypothesized in cosmology, physics, astronomy, religion, philosophy, transpersonal psychology, and fiction, particularly in science fiction and fantasy. In these contexts, parallel universes are also called "alternate universes", "quantum universes", "interpenetrating dimensions", "parallel dimensions", "parallel worlds", "alternate realities", "alternate timelines", and "dimensional planes", among other names.</p>
 43: <p>Buddha's response to such questions has been that whether or not other worlds exist, his teaching is still beneficial if applied in practice.</p>

<p>So, for example, if it is said that acting on an extreme negativity-rooted-in-confusion leads to hell, whether the hell is taken literally as a place you go to or metaphorically as a highly disagreeable state of subjective experience, in either case it is something a sane person would definitely prefer to avoid, and so refraining from acting out one's negativity rooted in confusion should be beneficial in either case.</p>

<p>While I personally lean towards <a href="https://buddhism.stackexchange.com/a/11485/43">a more "secular" view</a>, I feel that by shifting my focus from the metaphysics ("how things are") and towards soteriological methodology ("how to act towards Bodhi") I can avoid hurtful and non-productive arguments in the public space.</p>
